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# Scores on a standardized test are approximately normally ISBN: 9780073401331 38

## Solution for problem 7E Chapter 4.5

Statistics for Engineers and Scientists | 4th Edition

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Problem 7E

Scores on a standardized test are approximately normally distributed with a mean of 480 and a standard deviation of 90.

a. What proportion of the scores are above 700?

b. What is the 25th percentile of the scores?

c. If someone's score is 600, what percentile is she on?

d. What proportion of the scores are between 420 and 520?

Step-by-Step Solution:

Step 1 of 4:

Let X denote the score on a standardized test.

Then it is approximately normally distributed with mean is 480 and standard deviation is 90.

Our goal is:

a). We need to find the proportion of the scores are above 700.

b). We need to find the probability of the 25th percentile of the scores.

c). If someone’s score is 600 and we need to find the percentile is she on.

d). We need to find the the proportion of the scores are between 420 and 520.

a).

Now we have to find the proportion of the scores are above 700.

Here X is 700.

Then we have to calculate .

So P(X>700)=1-P(X 700).

P(X>700)=1-P(z 700)

The formula of the z is

z= We know that mean 480 and standard deviation 90.

Then,    = 1- Using area under the normal curve table. = 0.9927. = 1- 0.9927 = 0.0073

Therefore the probability that a battery will last more than 19 hours is 0.0073.

Step 2 of 4:

b).

Now we have to find the probability of the 25th percentile of the scores.

The z score of the 25th percentile it is corresponding to the -0.67 on the chart book.

Then the formula of the z is

z= We know that z value is -0.67.

-0.67=  =(-0.67)(90)

X= 480-60.3

X= 419.7

Therefore the probability of the 25th percentile of the scores is 419.7.

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073401331

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