Chapter 2.2, Problem 67E

(a)

To determine

To find: the percent scores greater than 27.

Answer to Problem 67E

The percent scores greater than 27 is 11.47%

Explanation of Solution

Given:

Mean is 21.2

Standard deviation is 5.0

149,164 had scores higher than 27

50,510 had scores exactly 27.

There is no area exactly above 27

Calculation:

The percent of scores above 27 is:

  $\begin{array}{c}\frac{149,164}{1,300,599}=0.1147\\ =11.47\%\end{array}$

Conclusion:

Therefore, the percent scores greater than 27 is 11.47%

(b)

To determine

To find: the percent scores greater than or equal to 27

Answer to Problem 67E

The percent scores greater than or equal to 27is 15.34%

Explanation of Solution

Calculation:

The percent of scores greater than or equal to 27 is:

  $\begin{array}{c}\frac{149,164+50,310}{1,300,599}=0.1534\\ =15.34\%\end{array}$

Conclusion:

Therefore, the percent scores greater than or equal to 27 is 15.34%

(c)

To determine

To find: the percent of observations which are greater than or equal to 27

Answer to Problem 67E

12.30% of scores would be 27 or higher

Explanation of Solution

Calculation:

For the $N\left(21.2,5.0\right)$ , the percent of observations greater than 27 corresponds to the percent of observations above:

  $\begin{array}{l}z=\frac{27-21.2}{5}\\ =1.16\text{on the Standard Normal Curve}\text{.}\end{array}$

Using normal distribution table, this proportion is 0.1230.

So, about 12.30% of scores would be 27 or higher

Conclusion:

Therefore, 12.30% of scores would be 27 or higher