Q$5.$H$.$W The amount of time that customers using ATM $($Automatic Teller Machine$)$ is a random variable with a standard deviation of $1\mathrm{.}4$ minutes. If we wish to estimate the population mean $m$ by the sample mean $\stackrel{}{x},$ and if we want to be $96\%$ confident that the sample mean will be within $0\mathrm{.}3$ minutes of the population mean, then the sample size needed is $($A$)98($B$)100($C$)92($D$)85$

Q$6$ H$.$W A random sample of size $n=36$ from a normal quantitative population produced a mean $\stackrel{}{x}=15\mathrm{.}2$ and a variance $S^2=9.$

$($a$)$ Give a point estimate for the population mean $m.$

$($b$)$ Find a $95\%$ confidence interval for the population mean $m.$

Q$7.$H$.$W A group of $10$ college students were asked to report the number of hours that they spent doing their homework during the previous weekend and the following results were obtained:

$7\mathrm{.}25,8\mathrm{.}5,5\mathrm{.}0,6\mathrm{.}75,8\mathrm{.}0,5\mathrm{.}25,10\mathrm{.}5,8\mathrm{.}5,6\mathrm{.}75,9\mathrm{.}25$

${\displaystyle \underset{?}{\overset{?}{}}}x=75\mathrm{.}75,{\displaystyle \underset{?}{\overset{?}{}}}{x}^2=600\mathrm{.}563$

It is assumed that this sample is a random sample from a normal distribution with unknown variance $S^2.$ Let $m$ be the mean of the number of hours that the college student spend doing his$/$her homework during the weekend.

$($a$)$ Find the sample mean and the sample variance.

$($b$)$ Find a point estimate for $m.$

$($c$)$ Construct a $80\%$ confidence interval for $m.$