Video In the EAI sampling problem, the population mean is $51,400 and the popula

Question

Video In the EAI sampling problem, the population mean is $51,400 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. a. What is the probability that the sample mean is within $600 of the population mean if a sample of size 40 is use (to 4 decimal? 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

Let X= sample mean

a. Sample size =40

X has a normal distribution with mean =51,400 and sd =5,000/40=790.569

Z=(X-51,400)/790.569 has a standard normal distribution

P(52,000<X<50,800)=P(-0.7589<Z<0.7589)=0.5521

b. Sample size =80

X has a normal distribution with mean =51,400 and sd =5,000/80=559.017

Z=(X-51,400)/559.017 has a standard normal distribution

P(52,000<X<50,800)=P(-1.0733<Z<1.0733)=0.7169

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