Chapter 14.5, Problem 29E

a.

To determine

Find the standard error of the mean.

Answer to Problem 29E

  $4.5$

Explanation of Solution

Given information:

Given: One hundred bulbs are selected randomly. The time to burn out for each bulb has been recorded. The average life is $350hours$ with a standard deviation of $45hours$ .

Calculation:

Here, we have to find the standard error of the mean:

  $\begin{array}{l}{\sigma }_{\overline{X}}=\frac{Standarddeviation}{\sqrt{N}}\\ {\sigma }_{\overline{X}}=\frac{45}{\sqrt{100}}=4.5\end{array}$

Hence, the standard error of the mean is $4.5$ .

b.

To determine

Find the interval about the sample mean having $1\%$ confidence level.

Answer to Problem 29E

  $\left[338.39,361.61\right]$

Explanation of Solution

Given information:

Given: One hundred bulbs are selected randomly. The time to burn out for each bulb has been recorded. The average life is $350hours$ with a standard deviation of $45hours$ .

Calculation:

Here, we have to find the interval:

  $\begin{array}{l}1\%confidencelevelmeansP=99\%\\ P=99\%correspondstot=2.58\\ \left[\overline{X}-t{\sigma }_X,\overline{X}+t{\sigma }_X\right]\\ \left[338.39,361.61\right]\end{array}$

Hence, the interval is $\left[338.39,361.61\right]$ .

c.

To determine

Find the number used as average lifetime of the bulbs.

Answer to Problem 29E

  $338hours$

Explanation of Solution

Given information:

Given: One hundred bulbs are selected randomly. The time to burn out for each bulb has been recorded. The average life is $350hours$ with a standard deviation of $45hours$ .

Calculation:

Here, we have to choose an average lifetime outside the interval $\left[338.39,361.61\right]$ having $1\%$ chance that the mean is less than this number.

Hence, the required answer is $338hours$ .