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In the EAI sampling problem, the population mean is $71,000 and the population standard deviation is $4,000 . For n=20 , there is a 0.4246 probability of obtaining a sample mean within of the population mean. Use *z*-table.

**a.** What is the probability that x is within $500 of the population mean if a sample of size 40 is used (to 4 decimals)?

**b.** Answer part (a) for a sample of size 80 (to 4 decimals).

Given that, mean( ?) = 71,000 standard deviation( ?) = 4000 sample size(n1) = 20 population mean(E) = 500 the value of z is calculated by using below