73. Sunshine City was designed to attract retired people, and its current popula

Question

73. Sunshine City was designed to attract retired people, and 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. (a) What is the distribution of the sample mean age of residents for a random sample of 100 residents? 50 and 70 years of age? than 55? (b) What is the probability that a random sample of 100 residents have a mean age between (e) What is the probability that the mean age of a random satmple of 100 residents is less

Explanation / Answer

a) here as sample size is greater than 30 therefore from central limit theorum ; sampling distribution of mean is approximately normal

with mean =60

and std error of mean =std deviation/(n)1/2 =16/(100)1/2 =1.6

b)

c)

for normal distribution z score =(X-)/ here mean=       = 60 std deviation   == 1.6000

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