In the EAI sampling problem, the population mean is $51,200 and the population s
ID: 3356226 • Letter: I
Question
In the EAI sampling problem, the population mean is $51,200 and the population standard deviation is $5,000. When the sample size is n = 20, there is a 0.4108 probability of obtaining a sample mean within +/- $600 of the population mean.
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) here std error =std deviation/(n)1/2 =5000/(40)1/2 =790.57
therefore probability that the sample mean is within $600 of the population mean=P(-600/790.57<Z<600/790.57)
=P(-0.76<Z<0.76)=0.7764-0.2236 =0.5527
b)
std error =std deviation/(n)1/2 =5000/(80)1/2 =559.02
therefore probability that the sample mean is within $600 of the population mean=P(-600/559.02<Z<600/559.02)
=P(-1.07<Z<1.07)=0.8577-0.1423 =0.7154