Question

A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 41 years old, with a standard deviation of 12 years. Suppose that these measures are valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers.

(a) According to Chebyshev's theorem, at least 36% of the home buyers' ages lie between ______ years and _______ years. (Round your answer to the nearest integer.)

(b) According to Chebyshev's theorem, at least ________ (56% 75% 84% or 89%) of the home buyers' ages lie between 17 years and 65.

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately _______ (68% 75% 95% or 99.7%) of the home buyers' ages lie between 17 years and 65.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the home buyers' ages lie between

years _______ and _________ years.

Answer 1

sample size,n = 1000

sample mean,x = 41

standard deviation,s = 12

a)

1 - (1 / k^2) = 0.36

k = 1.25

at least 36% of the lifetimes lie between (x - ks) and (x + ks) hours = [41-1.25*12,41+1.25*12]

26 years and 56 years

b)

65 = x + 2s

17= x - 2s

so k = 2

1 - (1 / k^2) = 0.75

at least 75%

c)

95% values lies within 2*standard deviation from mean

d)

99.7% values lies within 3*standard deviation from mean

x - 3s = 5

x + 3s = 77

approximately 99.7% of the lifetimes lie between 6 years and 77 years