Question

Assume the average life-span of those born in the U.S. is 78.2 years with a standard deviation of 16 years. The distribution is not normal (it is skewed left). The good people at Live-Longer-USA (fictitious) claim that their regiment of acorns and exercise results in longer life. So far, 50 people on this program have died and the mean age-of-death was 83.9 years.

(a) Calculate the probability that a random sample of 50 people from the general population would have a mean age-of-death greater than 83.9 years. Round your answer to 4 decimal places.

(b) Which statement best describes the situation for those in the Live Longer program?

This provides solid evidence that acorns and exercise cause people to live longer.

Since the probability of getting a sample of 50 people with a mean age-of-death greater than those in the Live Longer program is so small, this suggests that people enrolled in the program do actually live longer on average.

This provides solid evidence that acorns and exercise have nothing to do with age-of-death.

(c) Why could we use the central limit theorem here despite the parent population being skewed?

Because the sample size is greater than 30.

Because the sample size is greater than 20.

Because skewed-left is almost normal.

Because the sample size is less than 100.

Answer 1

Answer)

According to the central limit theorem, if sample size is greater than 30, we can assume normality.

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/(s.d/√n)

Given mean = 78.2

S.d = 16

N = 50

A)

P(x>83.9)

Z = (83.9 - 78.2)/(16/√50) = 2.52

From z table, P(z>2.52) = 0.0059

B)

Since the probability of getting a sample of 50 people with a mean age-of-death greater than those in the Live Longer program is so small, this suggests that people enrolled in the program do actually live longer on average.

C)

Because the sample size is greater than 30