In 2013, 4579 runners completed the Great Cow Harbor 10K Run in Northport, New York. Their age distribution has mean 40.2 years and standard deviation 12.4 years.

a. Assuming the distribution is normally distributed, find the probability that a randomly selected runner’s age was

i. Between 40 and 50 years.

ii. Between 30 and 60 years.

iii. Between 20 and 70 years.

b. A density histogram of the ages is shown in Fig. 91. Describe the shape of the distribution.

c. Use the density histogram to estimate the probability that a randomly selected runner’s age was

i. Between 40 and 50 years.

ii. Between 30 and 60 years.

iii. Between 20 and 70 years.

d. Compare the results you found in part (c) with the results you found in part (a). On the basis of your comparison and your response to part (b), determine whether the distribution is approximately normal.

Transcribed Image Text:

Ages of Runners 0.04 0.03 0.02 0.30 0.26 0.01 0.18 0.16 0.05 0.04 10 20 30 40 50 60 70 80 90 Age (years)