Question 1

According to the Empirical Rule, what percentage of values will be contained  between one standard deviation below the mean and one standard deviation above  the mean?

1. 34%
2. 50%
3. 68%

Question 2

According to the Empirical Rule, what percentage of values will be contained  between one standard deviation below the mean and one standard deviation above  the mean?

Which of the following describes what the numbers on the following graph (1, 2, 3, etc.) represent?

1. Z-scores
2. Standard Deviation
3. Number of occurrences
4. Probability

Hint: Review the standard normal curve.

Question 3

At the top of the DCMP Normal Distribution tool, choose the Find Probability tab.

1. Let’s find the exact probability that a normally distributed random variable is  within one standard deviation of the mean.
   To find the probability that a random variable will be between two specified  values, set “Type of Probability” to “Interval: [latex]P(a < X < b)[/latex].” What is the probability that a random variable that has a standard normal  distribution will be between −1 and 1? Hint: Use the “Value of a” box to set your lower value and the “Value of b” box to set  your upper value. Remember that the shaded part of the graph represents the  probability.
2. What do you notice about your answer for Part a? Hint: Remember the Empirical Rule.

Question 4

Recall Question 3 from Practice Assignment 8.D. The average body temperature for  healthy adults is 98.2°F with a standard deviation of 0.73°F.

1. What is the probability a randomly selected healthy adult will have a  temperature below 98.6°F? Write your answer as a proportion. Include 4  decimal places in your answer.
   Hint: Use the lower tail probability.
2. What is the probability a randomly selected healthy adult will have a  temperature above 100.4°F?

   Hint: Use the upper tail probability.

3. A fever is considered medically significant if body temperature reaches  100.4°F. What do you observe about this temperature? Do you think this  temperature is medically significant?

   Hint: Think about z-scores. How many standard deviations above the mean is this  temperature?

Question 5

One thousand high school juniors take a standardized exam. The distribution of  student scores approximates a normal distribution with an average score of 68.4 and  a standard deviation of 6.8.

1. What percentage of students passed the exam with a score of at least 65? Hint: Use the upper tail probability.
2. Students who scored between 55 and 65 are given the chance to take the  exam again to improve their scores. What percentage of students will have  the chance to retake the exam?

   Hint: Use the interval probability.

3. Fill in the blanks. Round to the nearest hundredth.

   Approximately 68% of all scores are between _____ and _____.

   Approximately 95% of all scores are between _____ and _____.

   Approximately 99.7% of all scores are between _____ and _____.

   Hint: Remember the Empirical Rule.

4. On their score reports, students are told how their scores compare to other  students’ scores. For example, a student might be told that they scored  better than 80% of their peers. We can use this information to estimate the  students’ raw scores.
   At the top of the DCMP Normal Distribution tool, choose the Find

   Percentile/Quantile tab. Set the mean to 68.4 and the standard deviation to  6.8. Use the tool to complete the following table. Round to the nearest  hundredth.

5. Student Scored Better Than [latex]x[/latex]% of  Peers	Approximate Raw Score
   5%
   20%
   80%
   99%

   Hint: Use the lower tail option to calculate the percentile.