The average age of residents in a large residential retirement community is 69 y

Question

The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. Assume the age of residents in this community is normally distributed.

a. What is the probability of randomly selected a resident that is older than 75? Show work
b. Suppose a random sample of 35 residents is to be selected, and the sample mean age x of these residents is to be computed. What is the probability that the mean age for this sample is less than 67 years? Show work.

Explanation / Answer

Mean is 69 and SD is 5.8

A. P(x>75)=P(z>(75-69)/5.8) = P(Z>1.03) or 1-P(z<1.03)= 1-0.8485= 0.1514 from the normal distribution table

B. The sample mean will be same as 69

Standard error is given by 5.8/sqrt(35)= 0.98

Thus P(x<67)=P(z<(67-69)/0.98)=P(z<-2.04)=1-P(z<2.04)= from normal distribution table we get 1-0.9793= 0.0207

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