# Question: A study investigating the relationship between age and annual medical

A study investigating the relationship between age and annual medical expenses randomly samples 100 individuals in Davis, California. It is hoped that the sample will have a similar mean age as the entire population.

a. If the standard deviation of the ages of all individuals in Davis is σ = 15, find the probability that the mean age of the individuals sampled is within two years of the mean age for all individuals in Davis. (Find the sampling distribution of the sample mean age and use the central limit theorem. You don’t have to know the population mean to answer this, but if it makes it easier, use a value such as μ = 30.)

b. Would the probability be larger, or smaller, if σ = 10? Why?

a. If the standard deviation of the ages of all individuals in Davis is σ = 15, find the probability that the mean age of the individuals sampled is within two years of the mean age for all individuals in Davis. (Find the sampling distribution of the sample mean age and use the central limit theorem. You don’t have to know the population mean to answer this, but if it makes it easier, use a value such as μ = 30.)

b. Would the probability be larger, or smaller, if σ = 10? Why?

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