Question

Lifespan: 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, 35 people on this program have died and the mean age-of-death was 82.9 years.

(a) Calculate the probability that a random sample of 35 people from the general population would have a mean age-of-death greater than 82.9 years. Round your answer to 4 decimal places.


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

Since the probability of getting a sample of 35 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.      This provides solid evidence that acorns and exercise cause people to live longer.

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

A. Because the sample size is less than 100.

B. Because the sample size is greater than 20.     

C. Because the sample size is greater than 30.

D. Because skewed-left is almost normal.

Answer 1

(a)

= 78.2'

= 16

n = 35

SE = /

=16/

= 2.7045

To find P(>82.9):

Z = (82.9 - 78.2)/2.7045

= 1.7378

Table of Area Under Standard Normal Curve gives area = 0.4591

So,

P(>82.9)= 0.5 - 0.4591 =0.0409

So,

Answer is:

0.0409

(b)

Correct option:

Since the probability of getting a sample of 35 people with a mean age of death greater than those in the Live Longer program is so small, this suggests that people in the program do actually live longer on average.

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

(c)

Correct option:

C. Because the sample size is greater than 30.