{"id":1541,"date":"2022-01-18T21:52:50","date_gmt":"2022-01-18T21:52:50","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=1541"},"modified":"2022-02-08T04:56:25","modified_gmt":"2022-02-08T04:56:25","slug":"8b","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/8b\/","title":{"raw":"8B","rendered":"8B"},"content":{"raw":"<div align=\"center\">\r\n\r\n<img class=\"alignnone wp-image-1542\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215042\/Picture189-300x245.png\" alt=\"A table with one column labeled Response and another labeled Frequency. The first row says &quot;0 Days&quot; under response and 157 under Frequency. The next row reads &quot;1 to 4 Days&quot; under Response and 6191 under Frequency. Under Response, it reads &quot;5 to 10 Days&quot; and under Frequency, it reads 6819. It reads &quot;11 to 14 Days&quot; under Response and 12838 under Frequency. Lastly, it reads &quot;Total&quot; and then under Frequency, it says &quot;26005.&quot;\" width=\"1072\" height=\"879\" \/><img class=\"alignnone wp-image-1543\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215047\/Picture192-300x102.png\" alt=\"A bar graph with a horizontal axis labeled &quot;Number of days&quot; and a vertical axis labeled &quot;Count&quot; and numbered in increments of 5 thousand. For 0, the count is 15754. For 1, the count is 5061. For 2, the count is 5585. For 3, the count is 5094. For 4, the count is 2708. For 5, the count is 2388. For 6, the count is 1143. For 7, the count is 799.\" width=\"1006\" height=\"342\" \/><img class=\"alignnone wp-image-1544\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215052\/Picture20-300x104.png\" alt=\"A bar chart labeled &quot;Number of servings per day&quot; on the horizontal axis and &quot;Count&quot; on the vertical axis, and numbered in increments of five thousand. For 0, the count is 6125. For 1-2, the count is 25290. For 3-4, the count is 6023. For 5-6, the count is 774. For more than 6, the count is 254.\" width=\"1015\" height=\"352\" \/><img class=\"alignnone wp-image-1553\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215756\/Picture213-300x123.png\" alt=\"A bar chart with &quot;M, Number of free throws made&quot; on the horizontal axis and &quot;Probability&quot; on the vertical axis. For 0 and 1, the probability is 0. For 2, the probability is 0.0002. For 3, the probability is 0.0015. For 4, the probability is 0.0092. For 5, the probability is 0.0387. For 6, the probability is 0.1131. For 7, the probability is 0.2265. For 8, the probability is 0.2977. For 9, the probability is 0.2318. For 10, the probability is 0.0812.\" width=\"1078\" height=\"442\" \/><img class=\"alignnone wp-image-1546\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215101\/Picture221-300x121.png\" alt=\"A bar chart showing &quot;C, Number of free throws made by Stephen Curry&quot; on the x-axis and &quot;Probability&quot; on the y-axis. For 0 through 3, the probability is 0. For 4, the probability is 0.0001. For 5, the probability is 0.0011. For 6, the probability is 0.0087. For 7, the probability is 0.0487. For 8, the probability is 0.1783. For 9, the probability is 0.3863. For 10, the probability is 0.3768.\" width=\"1004\" height=\"405\" \/><img class=\"alignnone wp-image-1547\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215105\/Picture23-300x200.jpg\" alt=\"A student napping on a desk in a classroom.\" width=\"1010\" height=\"673\" \/><img class=\"alignnone wp-image-1548\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215110\/Picture241-300x110.png\" alt=\"A bar chart labeled &quot;X, number of days that included a nap&quot; on the horizontal axis&quot; and &quot;P(X)&quot; on the vertical axis. For 0, P(X) is 0.361. For 1, P(X) is 0.195. For 2, P(X) is 0.165. For 3, P(X) is 0.107. For 4, P(X) is 0.058. For 5, P(X) is 0.045. For 6, P(X) is 0.023. For 7, P(X) is 0.045.\" width=\"1298\" height=\"476\" \/><img class=\"alignnone wp-image-1549\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215114\/Picture251-300x152.png\" alt=\"A bar chart labeled &quot;X, Number of Tails in Three Flips of a Coin&quot; on the horizontal axis and &quot;P(X)&quot; on the y-axis. For 0, P(X) is 0.125. For 1, P(X) is 0.375. For 2, P(X) is 0.375. For 3, P(X) is 0.125.\" width=\"1028\" height=\"521\" \/>\r\n\r\n<img class=\"alignnone wp-image-1550\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215120\/Picture261-300x123.png\" alt=\"A bar chart labeled &quot;X, Response to the survey question&quot; on the horizontal axis and &quot;P(X)&quot; on the vertical axis. For &quot;Did not do this activity,&quot; P(X) is 0.613. For &quot;Never,&quot; P(X) is 0.178. For &quot;Rarely,&quot; P(X) is 0.044. For &quot;Sometimes,&quot; P(X) is 0,033. For &quot;Most of the time,&quot; P(X) is 0.037. For &quot;Always,&quot; P(X) is 0.095.\" width=\"1050\" height=\"430\" \/>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Response<\/strong><\/td>\r\n<td><strong>Frequency<\/strong><\/td>\r\n<td><strong>Proportion \/ Relative Frequency<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0 Days<\/td>\r\n<td>157<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 to 4 Days<\/td>\r\n<td>6,191<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5 to 10 Days<\/td>\r\n<td>6,819<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>11 to 14 Days<\/td>\r\n<td>12,838<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Total:<\/strong><\/td>\r\n<td><strong>26,005<\/strong><\/td>\r\n<td><strong>1<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Servings per day<\/strong><\/td>\r\n<td><strong>Frequency<\/strong><\/td>\r\n<td><strong>Proportion \/ Relative Frequency<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 to 2<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3 to 4<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5 to 6<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>More than 6<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Total:<\/strong><\/td>\r\n<td><strong>\u00a0<\/strong><\/td>\r\n<td><strong>\u00a0<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>, Number of days<\/strong><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0.336<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>0.231<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>0.143<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>0.085<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>0.051<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>0.053<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td>0.028<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>7<\/td>\r\n<td>0.074<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>, Number of free throws made<\/strong><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0.0000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>0.0000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>0.0002<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>0.0015<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>0.0092<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>0.0387<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td>0.1131<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>7<\/td>\r\n<td>0.2265<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>8<\/td>\r\n<td>0.2977<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>9<\/td>\r\n<td>0.2318<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>10<\/td>\r\n<td>0.0812<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>, Number of days that included a nap<\/strong><\/td>\r\n<td><strong>Frequency<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>7<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>TOTAL:<\/strong><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>, Number of days that included a nap<\/strong><\/td>\r\n<td><strong>,<\/strong>\r\n\r\n<strong>The probability of randomly selecting an individual who stated <\/strong><strong>\u00a0days with a nap<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>7<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>SUM:<\/strong><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Experimental Outcome<\/strong><\/td>\r\n<td><strong>, Number of Tails in 3 Flips of a Coin<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>HHH<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>HHT<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>HTH<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>THH<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>TTH<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>THT<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>HTT<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>TTT<\/td>\r\n<td>3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>, Number of Tails in 3 Flips of a Coin<\/strong><\/td>\r\n<td><strong>Frequency<\/strong><\/td>\r\n<td><strong>Relative Frequency<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>1<\/td>\r\n<td>0.125<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Total:<\/strong><\/td>\r\n<td><strong>8<\/strong><\/td>\r\n<td><strong>1<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>, Number of days<\/strong><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0.336<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>0.231<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>0.143<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>0.085<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>0.520<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>0.053<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td>0.028<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>7<\/td>\r\n<td>0.074<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>, Number of days<\/strong><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0.4974<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>0.1811<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>0.1391<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>0.0729<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>0.0377<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>0.0325<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td>0.012<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>7<\/td>\r\n<td>0.0271<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Skill or Concept: I can . . .<\/strong><\/td>\r\n<td><strong>Questions to check your understanding<\/strong><\/td>\r\n<td><strong>Rating\r\nfrom 1 to 5<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Make connections between frequency, relative frequency, and probability.<\/td>\r\n<td>1<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Interpret discrete probability distributions to calculate probabilities, including those involving the phrases OR, at least, at most, less than, and greater than.<\/td>\r\n<td>2<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify whether a table or graph represents a probability distribution for a discrete random variable.<\/td>\r\n<td>3<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nGlossary\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<dl id=\"fs-id1170572229168\" class=\"definition\">\r\n \t<dt>discrete random variable<\/dt>\r\n \t<dd id=\"fs-id1170572229174\">a variable that takes a fixed set of possible numerical values and it is not possible to get any value in between.<\/dd>\r\n<\/dl>","rendered":"<div style=\"margin: auto;\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1542\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215042\/Picture189-300x245.png\" alt=\"A table with one column labeled Response and another labeled Frequency. The first row says &quot;0 Days&quot; under response and 157 under Frequency. The next row reads &quot;1 to 4 Days&quot; under Response and 6191 under Frequency. Under Response, it reads &quot;5 to 10 Days&quot; and under Frequency, it reads 6819. It reads &quot;11 to 14 Days&quot; under Response and 12838 under Frequency. Lastly, it reads &quot;Total&quot; and then under Frequency, it says &quot;26005.&quot;\" width=\"1072\" height=\"879\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1543\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215047\/Picture192-300x102.png\" alt=\"A bar graph with a horizontal axis labeled &quot;Number of days&quot; and a vertical axis labeled &quot;Count&quot; and numbered in increments of 5 thousand. For 0, the count is 15754. For 1, the count is 5061. For 2, the count is 5585. For 3, the count is 5094. For 4, the count is 2708. For 5, the count is 2388. For 6, the count is 1143. For 7, the count is 799.\" width=\"1006\" height=\"342\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1544\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215052\/Picture20-300x104.png\" alt=\"A bar chart labeled &quot;Number of servings per day&quot; on the horizontal axis and &quot;Count&quot; on the vertical axis, and numbered in increments of five thousand. For 0, the count is 6125. For 1-2, the count is 25290. For 3-4, the count is 6023. For 5-6, the count is 774. For more than 6, the count is 254.\" width=\"1015\" height=\"352\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1553\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215756\/Picture213-300x123.png\" alt=\"A bar chart with &quot;M, Number of free throws made&quot; on the horizontal axis and &quot;Probability&quot; on the vertical axis. For 0 and 1, the probability is 0. For 2, the probability is 0.0002. For 3, the probability is 0.0015. For 4, the probability is 0.0092. For 5, the probability is 0.0387. For 6, the probability is 0.1131. For 7, the probability is 0.2265. For 8, the probability is 0.2977. For 9, the probability is 0.2318. For 10, the probability is 0.0812.\" width=\"1078\" height=\"442\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1546\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215101\/Picture221-300x121.png\" alt=\"A bar chart showing &quot;C, Number of free throws made by Stephen Curry&quot; on the x-axis and &quot;Probability&quot; on the y-axis. For 0 through 3, the probability is 0. For 4, the probability is 0.0001. For 5, the probability is 0.0011. For 6, the probability is 0.0087. For 7, the probability is 0.0487. For 8, the probability is 0.1783. For 9, the probability is 0.3863. For 10, the probability is 0.3768.\" width=\"1004\" height=\"405\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1547\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215105\/Picture23-300x200.jpg\" alt=\"A student napping on a desk in a classroom.\" width=\"1010\" height=\"673\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1548\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215110\/Picture241-300x110.png\" alt=\"A bar chart labeled &quot;X, number of days that included a nap&quot; on the horizontal axis&quot; and &quot;P(X)&quot; on the vertical axis. For 0, P(X) is 0.361. For 1, P(X) is 0.195. For 2, P(X) is 0.165. For 3, P(X) is 0.107. For 4, P(X) is 0.058. For 5, P(X) is 0.045. For 6, P(X) is 0.023. For 7, P(X) is 0.045.\" width=\"1298\" height=\"476\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1549\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215114\/Picture251-300x152.png\" alt=\"A bar chart labeled &quot;X, Number of Tails in Three Flips of a Coin&quot; on the horizontal axis and &quot;P(X)&quot; on the y-axis. For 0, P(X) is 0.125. For 1, P(X) is 0.375. For 2, P(X) is 0.375. For 3, P(X) is 0.125.\" width=\"1028\" height=\"521\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1550\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/18215120\/Picture261-300x123.png\" alt=\"A bar chart labeled &quot;X, Response to the survey question&quot; on the horizontal axis and &quot;P(X)&quot; on the vertical axis. For &quot;Did not do this activity,&quot; P(X) is 0.613. For &quot;Never,&quot; P(X) is 0.178. For &quot;Rarely,&quot; P(X) is 0.044. For &quot;Sometimes,&quot; P(X) is 0,033. For &quot;Most of the time,&quot; P(X) is 0.037. For &quot;Always,&quot; P(X) is 0.095.\" width=\"1050\" height=\"430\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>Response<\/strong><\/td>\n<td><strong>Frequency<\/strong><\/td>\n<td><strong>Proportion \/ Relative Frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td>0 Days<\/td>\n<td>157<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>1 to 4 Days<\/td>\n<td>6,191<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>5 to 10 Days<\/td>\n<td>6,819<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>11 to 14 Days<\/td>\n<td>12,838<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>Total:<\/strong><\/td>\n<td><strong>26,005<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>Servings per day<\/strong><\/td>\n<td><strong>Frequency<\/strong><\/td>\n<td><strong>Proportion \/ Relative Frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>1 to 2<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>3 to 4<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>5 to 6<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>More than 6<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>Total:<\/strong><\/td>\n<td><strong>\u00a0<\/strong><\/td>\n<td><strong>\u00a0<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>, Number of days<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0.336<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>0.231<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>0.143<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>0.085<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>0.051<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>0.053<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>0.028<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>0.074<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>, Number of free throws made<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0.0000<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>0.0000<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>0.0002<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>0.0015<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>0.0092<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>0.0387<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>0.1131<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>0.2265<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>0.2977<\/td>\n<\/tr>\n<tr>\n<td>9<\/td>\n<td>0.2318<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>0.0812<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>, Number of days that included a nap<\/strong><\/td>\n<td><strong>Frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>TOTAL:<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>, Number of days that included a nap<\/strong><\/td>\n<td><strong>,<\/strong><\/p>\n<p><strong>The probability of randomly selecting an individual who stated <\/strong><strong>\u00a0days with a nap<\/strong><\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>SUM:<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>Experimental Outcome<\/strong><\/td>\n<td><strong>, Number of Tails in 3 Flips of a Coin<\/strong><\/td>\n<\/tr>\n<tr>\n<td>HHH<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>HHT<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>HTH<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>THH<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>TTH<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>THT<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>HTT<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>TTT<\/td>\n<td>3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>, Number of Tails in 3 Flips of a Coin<\/strong><\/td>\n<td><strong>Frequency<\/strong><\/td>\n<td><strong>Relative Frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>1<\/td>\n<td>0.125<\/td>\n<\/tr>\n<tr>\n<td><strong>Total:<\/strong><\/td>\n<td><strong>8<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>, Number of days<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0.336<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>0.231<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>0.143<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>0.085<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>0.520<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>0.053<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>0.028<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>0.074<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>, Number of days<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0.4974<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>0.1811<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>0.1391<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>0.0729<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>0.0377<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>0.0325<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>0.012<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>0.0271<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>Skill or Concept: I can . . .<\/strong><\/td>\n<td><strong>Questions to check your understanding<\/strong><\/td>\n<td><strong>Rating<br \/>\nfrom 1 to 5<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Make connections between frequency, relative frequency, and probability.<\/td>\n<td>1<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Interpret discrete probability distributions to calculate probabilities, including those involving the phrases OR, at least, at most, less than, and greater than.<\/td>\n<td>2<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Identify whether a table or graph represents a probability distribution for a discrete random variable.<\/td>\n<td>3<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Glossary<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<dl id=\"fs-id1170572229168\" class=\"definition\">\n<dt>discrete random variable<\/dt>\n<dd id=\"fs-id1170572229174\">a variable that takes a fixed set of possible numerical values and it is not possible to get any value in between.<\/dd>\n<\/dl>\n","protected":false},"author":23592,"menu_order":29,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1541","chapter","type-chapter","status-publish","hentry"],"part":704,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1541","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1541\/revisions"}],"predecessor-version":[{"id":2914,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1541\/revisions\/2914"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/704"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1541\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=1541"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=1541"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=1541"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=1541"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}