Rainbow City was designed to attract orphan children.

Its current population of 30,000 children has a mean age of 6 years and a standard deviation of 10 years. The distribution of ages is skewed to the left, reflecting the predominance of older children. A random sample of 100 children of Rainbow City has ¯y = 8.3 and s = 7.0.

(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 child of age 5 years in Rainbow City, but it would be highly unusual to observe a sample mean of 5, for a random sample size of 100.