# 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{

In the EAI sampling problem, the population mean is $71,500 and the population standard deviation is$5000. For of the population mean.
a) What is the probability that $\overline{x}$ 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). You can still ask an expert for help Expert Community at Your Service • Live experts 24/7 • Questions are typically answered in as fast as 30 minutes • Personalized clear answers Solve your problem for the price of one coffee • Available 24/7 • Math expert for every subject • Pay only if we can solve it ## Expert Answer Sadie Eaton Answered 2021-02-09 Author has 104 answers a) The probability that $\overline{x}$is within$600 of the population mean if a sample of size 60 used is,
$P\left(-600<\stackrel{―}{x}-\mu <600\right)=P\left(\frac{-600}{\left(\frac{5.000}{\sqrt{60}}\right)}<\frac{\stackrel{―}{x}-\mu }{\left(\frac{\sigma }{\sqrt{n}}\right)}<\frac{600}{\left(\frac{5.000}{\sqrt{60}}\right)}\right)$
$=P\left(\frac{-600}{645.4972}
$=P\left(-0.93
$=P\left(z<0.93\right)-P\left(z<-0.93\right)$
The probability of z less than The probability value is 0.1762.
The probability of z less than . The probability value is 0.8238.
The required probability value is,
$P\left(-600<\stackrel{―}{x}-\mu <600\right)=P\left(z<0.93\right)-P\left(z<-0.93\right)$

$=0.6476$
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,
$P\left(-600<\stackrel{―}{x}-\mu <600\right)=P\left(\frac{-600}{\left(\frac{5.000}{\sqrt{120}}\right)}<\frac{\stackrel{―}{x}-\mu }{\left(\frac{\sigma }{\sqrt{n}}\right)}<\frac{600}{\left(\frac{5.000}{\sqrt{120}}\right)}\right)$
$=P\left(\frac{-600}{456.4355}
$=P\left(-1.31
$=P\left(z<1.31\right)-P\left(z<-1.31\right)$
The probability of z less than The probability value is 0.0951.
The probability of z less than The probability value is 0.9049.
The required probability value is,