Question

Authors L sievert and Hautaniemi compared the age of menopause for different populations. Menopause the last menstrual period is a universal phenomenon among females. According to the article the mean age of menopause, surgical or natural, in Puebla, Mexico is 44.8 years with a standard deviation of 5.87 years. A simple random sample is take of 60 females in Puebla, Mexico.

a.) is it reasonable to assume a normal shape for the sampling distribution? Explain.

b.) Find the probability that a sample mean age of menopause (for a sample of size 60) is less than 43.5 years.

Answer 1

Given,

According to the article the mean age of menopause, surgical or natural, in Puebla, Mexico is 44.8 years with a standard deviation of 5.87 years.

A simple random sample is take of 60 females in Puebla, Mexico

X; Age of menopause, surgical or natural, in Puebla, Mexico

Mean of X : = 44.8

standard deviation of X : = 5.87

a)

By Central limit, large samples(sample size : n) are taken from the population, sampling distribution of sample mean follows Normal distribution with mean and standard deviation

As the sample is 60 which considered large; it is reasonable to assume a normal shape for the sampling distribution

b) sampling distribution of sample mean: follows Normal distribution with mean and standard deviation

Probability that a sample mean age of menopause (for a sample of size 60) is less than 43.5 years = P(<43.5)

Z-score for 43.5 = (43.5 - )/ = (43.5 - 44.8)/0.7578 = -1.715

From standard normal tables,

P(Z< - 1.71) = 0.0436

P(Z< -1.72) = 0.0427

P(Z< -1.715) = (0.0436+0.0427)/2 = 0.04315

P(<43.5) = P(Z< -1.715) = 0.04315

Probability that a sample mean age of menopause (for a sample of size 60) is less than 43.5 years = 0.04315