Sunshine City was designed to attract retired people.

Its current population of 50,000 residents has a mean age of 60 years and a standard deviation of 16 years. The distribution of ages is skewed to the left, reflecting the predominance of older individuals. A random sample of 100 residents of Sunshine City has ¯y = 58.3 and s = 15.0.

(a) Describe the center and spread of the population distribution.

(b) Describe the center and spread of the sample data distribution.

What shape does it probably have?

(c) Find the center and spread of the sampling distribution of ¯y for n = 100. What shape does it have and what does it describe?

(d) Explain why it would not be unusual to observe a person of age 40 in Sunshine City, but it would be highly unusual to observe a sample mean of 40, for a random sample size of 100.