Question

In the EAI sampling problem, the population mean is $51,700 and the population standard deviation is $5,000. When the sample size is n = 20, there is a 0.4085 probability of obtaining a sample mean within +/- $600 of the population mean. Use z-table.

What is the probability that the sample mean is within $600 of the population mean if a sample of size 40 is used (to 4 decimals)?

What is the probability that the sample mean is within $600 of the population mean if a sample of size 80 is used (to 4 decimals)?

Answer 1

Ans:

a)

z=+/-600/(5000/sqrt(40))

z=+/-0.759

P(-0.759<z<0.759)=P(z<0.759)-P(z<-0.759)

=0.7761-0.2239=0.5521

b)

z=+/-600/(5000/sqrt(80))

z=+/-1.073

P(-1.073<z<1.073)=P(z<1.073)-P(z<-1.073)

=0.8584-0.1416=0.7168