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Assume that the height of a random male X is distributed normally with mean μ =...

Assume that the height of a random male X is distributed normally with mean μ = 71 inches and standard deviation σ = 4 inches.

A sample of n = 36 males is selected at random. Let p hat denote the proportion of individuals in the sample that are 71.2 inches or taller.

(i) What are the mean and standard error of p hat?

(ii) Find the 97.5th percentile of̂ p hat.

(iii) What is P(p hat̂ <0.5)?

Math   Statistics-And-Probability   
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