Chapter 6, Problem 33E

a)

To determine

To find the percent of times less than 109.78 seconds.

Answer to Problem 33E

Approximately 16% of times should have less than 109.78 seconds.

Explanation of Solution

Given:

  $\mu$ = 113.02

  $\sigma$ = 3.24

The Normal model is,

  

From Normal model, 109.78 is 1 standard deviation below the mean.

We know that 68% of the data are within 1 standard deviation of the mean. That is, 100-68 = 32% of the IQ scores are more than 1 standard deviation from the mean.

We know, the normal curve is symmetric about the mean then 16% is more than 1 standard deviation below the mean and 16% is more than 1 standard deviation above the mean.

Hence, approximately 16% of times should have less than 109.78 seconds.

b)

To determine

To find the actual percent of times less than 109.78 seconds.

Answer to Problem 33E

The roughly 3.77% of times are less than 109.78 seconds.

Explanation of Solution

Given:

  $\mu$ = 113.02

  $\sigma$ = 3.24

  

From given data, 2 out of 53 data values are less than 109.78.

  $\frac{2}{53}=0.0377=3.77\%$

Hence, roughly 3.77% of times are less than 109.78 seconds.

c)

To determine

To explain why two percentages don’t agree.

Answer to Problem 33E

The two percentages do not agree because the distribution of the data values is not perfectly Normal.

Explanation of Solution

Given:

  $\mu$ = 113.02

  $\sigma$ = 3.24

  

The two percentages do not agree because the distribution of the data values is not perfectly Normal.

d)

To determine

To create Histogram.

Answer to Problem 33E

The distribution is roughly right skewed.

Explanation of Solution

  

The distribution is roughly right skewed.