Question

Use the following distributions for the following questions where appropriate (i.e. looking at one gender or comparing genders, vs looking at all Americans). On average, women live longer than men, so male and female lifespans have distinct distributions. The mean lifespan of an American woman is 81.6 years, with a standard deviation of 13.9 years, and the mean lifespan for American men is 76.9 years, with a standard deviation of 13.7 years.

1) Two old friends are debating who is older, relative to other people of the same gender. Jeanne, a woman, is 122 years old, and Jiroemon, a man, is 116 years old. Which of the two of them is older relative to the distributions of their respective genders' lifespans?

2) All four of Sam's grandparents lived to be over 85, with a mean lifespan of 89 years old. This strikes Sam as unlikely. What is the probability that a random sample of 4 randomly selected Americans would have a mean lifespan of at least 89?

3) What are the percent chances that a random sample of 20 American women have a mean lifespan of more than 85 years?

Answer 1

For American women the lifespan is :

For American men the lifespan is :

1) We can find who is older by converting their age to the standard Z score using the formula.

For Jeanne :

For Jiroemon :

hence the standard Z score for Jeanne is greater than Jiroemon, clearly, Jeanne is older relative to the distributions of their respective genders' lifespans.

3) the probability that a random sample of 20 American women have a mean lifespan of more than 85 years:

in percentage, it is 13.70%