In the EAI sampling problem, the population mean is $ 71,500 and the population standard deviation is $5000. For n = 30, text{there is a} 0.4908 text{

alesterp 2021-02-08 Answered
In the EAI sampling problem, the population mean is $ 71,500 and the population standard deviation is $5000. For n=30, there is a 0.4908 probability of obtaining a sample mean within ± $ 600 of the population mean.
a) What is the probability that x¯ is within $ 600 of the population mean is a sample of size 60 is used (to 4 decimals)?
b) Answer part (a) for a sample of size 120 (to 4 decimals).
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Expert Answer

Sadie Eaton
Answered 2021-02-09 Author has 104 answers

a) The probability that x¯is within $600 of the population mean if a sample of size 60 used is,
P(600<xμ<600)=P(600(5.00060)<xμ(σn)<600(5.00060))
=P(600645.4972<z<60645.4972)
=P(0.93<z<0.93)
=P(z<0.93)P(z<0.93)
The probability of z less than 0.93 can be obtained using the excel formula =NORM.S.DIST(0.93,TRUE)". The probability value is 0.1762.
The probability of z less than 0.93 can be obtained using the excel formula =NORM.S.DIST(0.93,TRUE)". The probability value is 0.8238.
The required probability value is,
P(600<xμ<600)=P(z<0.93)P(z<0.93)
=0.9238  0.1762
=0.6476
Thus, the probability that x- is within $600 of the population mean if a sample of size 60 used is 0.6476.
b) The probability that x- is within $600 of the population mean if a sample of size 120 used is,
P(600<xμ<600)=P(600(5.000120)<xμ(σn)<600(5.000120))
=P(600456.4355<z<60456.4355)
=P(1.31<z<131)
=P(z<1.31)P(z<1.31)
The probability of z less than 1.31 can be obtained using the excel formula =NORM.S.DIST(1.31,TRUE)". The probability value is 0.0951.
The probability of z less than 1.31 can be obtained using the excel formula =NORM.S.DIST(1.31,TRUE)". The probability value is 0.9049.
The required probability value is,

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