12A Coreq

In the next preview assignment and in the next class, you will need to calculate and  interpret z-scores and use a data analysis tool to calculate normal probabilities.

Calculating and Interpreting z-scores 

Data collected by the Centers for Disease Control and Prevention show that the  average birthweight for babies in the United States is 7.17 pounds and the standard  deviation of birthweights is 1.30 pounds.[1]

Question 1

1) What birthweight is one standard deviation above the mean? What birthweight is one standard deviation below the mean?

Question 2

2) For each of the two answers you computed in Question 1, subtract the mean of 7.17  and then divide by the standard deviation of 1.30. In other words, calculate the  following for each birthweight value computed in Question 1:

Value − 7.17

1.30

Question 3

3) What birthweight is two standard deviations above the mean? What birthweight is  two standard deviations below the mean?

Question 4

4) For each of the two answers you computed in Question 3, subtract the mean of 7.17  and then divide by the standard deviation of 1.30. In other words, calculate the  following for each birthweight value computed in Question 3:

Value − 7.17

1.30

The values you calculated in Questions 2 and 4 are called z-scores or standardized  scores. A z-score measures a value’s distance from the mean in units of standard  deviation. A positive z-score indicates the value is above the mean, whereas a negative  z-score indicates the value is below the mean.

Question 5

5) What birthweight is 1.5 standard deviations below the mean? In other words, what  birthweight has a z-score of −1.5?

Question 6

6) A baby is classified as low birthweight if they weigh less than 5.5 pounds.[2] How  many standard deviations from the mean is 5.5 pounds?

Question 7

7) The Guinness Book of World Records reports that the heaviest baby ever recorded  weighed a massive 22 pounds![3] How many standard deviations from the mean is  this birthweight?

Probabilities as Areas Under the Normal Curve 

Question 8

8) In statistics, you are often interested in finding probabilities involving a normal distribution. These probabilities are calculated by finding the area under a normal  curve. Answer the following questions as a review.

a) What is the area under the entire normal curve?

b) What is the area under the normal curve to the left of the mean?

c) Suppose you know that the area to the left of a given z-score is 0.32. What is  the area to the right of that z-score?

  1. Centers for Disease Control and Prevention. (n.d.). Natality for 2016–2019 (expanded).  https://wonder.cdc.gov/controller/datarequest/D149;jsessionid=7AB7525C7DC02FF1F19D38C125AC ↵
  2. 2 Martin, J. A., Hamilton, B. E., Osterman, M. J. K., & Driscoll, A. K. (2021, March 23). Births: Final data  for 2019. National Vital Statistics Reports, 70(2), 1–50. https://www.cdc.gov/nchs/data/nvsr/nvsr70/nvsr70-02-508.pdf  ↵
  3. Guinness World Records. (n.d.). Heaviest birth. https://www.guinnessworldrecords.com/world records/heaviest-birth ↵