Answer with explanation:
Sample Population = 225
Standard Deviation =75 feet
We have to check , whether , the sample mean, will be within 10 feet of the population mean, 99.7%=0.997 of the time.
[tex]Z_{0.997}=0.83891[/tex]
[tex]Z_{0.997}=\frac{\bar X-\mu}{\sigma}\\\\0.83891=\frac{225 -\mu}{75}\\\\75 \times 0.83891=225 - \mu\\\\ \mu=225 - 62.92\\\\ \mu=162.08[/tex]
Sample Mean =162 feet (Approx)
Assuming sample sample size is 2 times of sample Population.That is from ,450 , Sample of 250 is chosen.
Since, within three standard deviation ,from mean on both sides, the whole Population lies.
So, population Mean=225
Difference between Population mean and Sample Mean
→225 - 162= 63
Therefore, the Sample mean and population mean does not differ by a value of 10.
→Sample mean does not lie, within 10 feet of the population mean.
⇒The given statement is" false",which is ,the sample mean will be within 10 feet of the population mean 99.7% of the time.
