Chapter 14, Problem 14.1AYK

a)

To determine

To find: The standard deviation of the sampling distribution.

Answer to Problem 14.1AYK

The standard deviation is 0.40.

Explanation of Solution

Given:

Population mean (µ)

Standard deviation (s) = 8

Sample size ( n ) = 400

Calculation:

The standard deviation of the sampling distribution is calculated as:

  $\begin{array}{c}\sigma =\frac{\sigma }{\sqrt{n}}\\ =\frac{8}{\sqrt{400}}\\ =0.40\end{array}$

Thus, the standard deviation is 0.40.

b)

To determine

To construct: A normal curve that explains the variability of in many samples for the -provided population. Also, find the missing number using the 68-99-99.7 rule

Explanation of Solution

Graph:

The figure could be constructed as:  

Calculation:

The margin of error could be constructed as:

  $\begin{array}{c}2\times \sigma =2\times 0.4=0.8\\ 2\times -\sigma =2\times 0.4=-0.8\end{array}$

The values of $\overline{x}$ will range from -0.8 to 0.8.

Using these values, the figure is:

  

c)

To determine

To construct: The interval below the sketch for one of $\overline{x}$ that is lying the shaded region and other lying outside the shaded region.

Explanation of Solution

Graph:

The figure could be constructed as:

  

d)

To determine

To find: The percent of all samples would the confidence interval $\overline{x}\pm m$ contain the true population mean $\mu =140$

Answer to Problem 14.1AYK

The percentage is 95%.

Explanation of Solution

Calculation:

The percent of all the samples that would fall in the computed confidence interval is 95%. In this case, m is 0.8 and $\mu =140$ about 95% of all the samples would be in the confidence interval.