In the EAI sampling problem, the population mean is $51,700 and the population s

Question

In the EAI sampling problem, the population mean is $51,700 and the population standard deviation is $4,000. When the sample size is n20, there is a 0.4977 probability of obtaining a sample mean within +- $600 of the population mean. Use z-table a. 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)? b. 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)?

Explanation / Answer

a) Mean=$51,700

SD= 4000

Sample Size=40

Let x= sample mean,

where x is have a normal distribution with mean =51,700 and sd =4,000/40= 632.456064

Z=(X-51,700)/632.456064 has a standard normal distribution

P(51,100<X<52,300)=P(-0.948682<Z<0.948682)=0.8264

b) sample size=80

Let x= sample mean,

where x is have a normal distribution with mean =51,700 and sd =4,000/80= 447.227

Z=(X-51,700)/447.227 has a standard normal distribution

P(51,100<X<52,300)=P(-1.3416<Z<1.3416)=0.9099.

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