Chapter 14.4, Problem 16E

a.

To determine

To describe the 92^nd percentile in terms of standard deviation.

Answer to Problem 16E

  ${(x-2)}^2=8{(y-3)}^2$

Explanation of Solution

Given:

The percentile scores on standardized test.

Calculation:

From the table on page no. 919 in text book it can be easily concluded that 92^nd percentile means that data are within $2$ standard deviations from the mean.

This means

  $92\%=X\pm 2\sigma$

Where $X$ is mean and $\sigma$ is standard deviation.

b.

To determine

To name the percentile of the student whose score is $0.8$ standard deviation above the mean?

Answer to Problem 16E

  $68\%$

Explanation of Solution

Given:

The percentile scores on standardized test.

Calculation:

From the table on page no. 919 in text book it can be easily concluded that about $68.3\%$ of data are within $1$ standard deviation from the mean.

Since here, score is $0.8$ standard deviation above the mean, therefore approximate percentile of the student will be $68\%$ .