?Simulation According to the National Center for Health Statistics, the common cold occurs at the rate of 23.6 colds per 100 people during the course o

Chapter 6, Problem 23

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Simulation According to the National Center for Health Statistics, the common cold occurs at the rate of 23.6 colds per 100 people during the course of a year in the 18- to 24-year-old age group. Let the random variable X represent the number of 18- to 24-year-olds out of a sample of 500 who have had a common cold in the past year.

(a) What is the expected number of colds for every 500 18- to 24-year-olds?

(b) Using statistical software, such as Minitab, simulates taking 100 random samples of size 500 from this population.

(c) Approximate the probability that at least 150 18- to 24-year-olds in a group of 500 will have experienced a common cold in the past year.

(d) Approximate the probability that fewer than 100 18- to 24-year-olds in a group of 500 will have experienced the common cold in the past year.

(e) Given the simulation, compute the mean number of 18- to 24-year-olds out of 500 who have experienced the common cold in the past year.

(f) Given the simulation, compute the standard deviation of the number of 18- to 24-year-olds out of 500 who have experienced the common cold in the past year.

(g) Compute the 5-number summary of the data. Did the simulation result in any unusual results?