Question

You draw samples of size n from the population of all pennies in circulation. The random variable of interest is the mean age of the pennies in the sample (current year pennies are considered to be zero years old). The distribution of ages of pennies (starting at 0) is known to be skewed markedly to the right. That is, there are more recently minted pennies than older pennies in the population. One scholar claims that the mean age of all pennies in circulation is 7.4 years with a standard deviation of 3.3 years. Assume that this scholar is correct. Discuss the mean, standard deviation, and shape of the sampling distribution of sample means of the ages of pennies for each of the given sample sizes. Where possible, give precise values. A. n = 5 B. n = 15 C. n = 40

Answer 1

Answers explained below

Explanation:

Let X be the random variable that ages of pennies.

Also given that distribution of X is skewed to the right.

Given that,

mean = 7.4 years

standard deviation, sd = 3.3 years

Discuss the mean, standard deviation, and shape of the sampling distribution of sample means of the ages of pennies for each of the given sample sizes.

For n = 5,

the mean of the sampling distribution of mean = 7.4

sd of the samplong distribution of mean = 3.3 / sqrt(5) = 1.48

Shape of the distribution is positively skewed.

For n= 15

the mean of the sampling distribution of mean = 7.4

sd of the samplong distribution of mean = 3.3 / sqrt(15) = 0.85

Shape of the distribution is positively skewed.

For n = 40

the mean of the sampling distribution of mean = 7.4

sd of the samplong distribution of mean = 3.3 / sqrt(40) = 0.52

Shape of the distribution is bell shaped or normal distribution.