Chapter 6, Problem 35E

a)

To determine

To find the percent of receivers that expect to gain fewer yards than 2 standard deviations below the mean number of yards.

Answer to Problem 35E

The 2.5% of the scores should be more than 2 standard deviations above the mean.

Explanation of Solution

Given:

  $\mu$ = 435

  $\sigma$ = 384

  

Following is the model which shows 68-95-99.7:

  

According to rule, 95% of the data lies between 2 standard deviations from the mean. Since, total data is 100%, so 5% of the data is the more than 2 standard deviations from the mean. Therefore, as per symmetry, 2.5% is more than 2 standard deviations below the mean and 2.5% is more than 2 standard deviations above the mean.

Hence, 2.5% of the scores should be more than 2 standard deviations above the mean.

b)

To determine

To explain the meaning from part a)

Answer to Problem 35E

2.5% values should be above 1203.

Explanation of Solution

Given:

  $\mu$ = 435

  $\sigma$ = 384

  

Following is the model which shows 68-95-99.7:

  

The 2.5% of the scores should be more than 2 standard deviations above the mean.

That means,

  $\mu +2\sigma =435+2\times 384=1203$

Since there are 167 values, $2.5\%\times 167=4.175$ values should be above 1203.

c)

To determine

To explain the problem in histogram using Normal model.

Answer to Problem 35E

It is not appropriate to use Normal model.

Explanation of Solution

Given:

  $\mu$ = 435

  $\sigma$ = 384

  

Following is the model which shows 68-95-99.7:

  

As per Histogram, the distribution is strongly right skewed, because the highest bars are to the left. Therefore, the given distribution is not approximately Normal distribution. Hence, it is not appropriate to use Normal model.