 # S O C The average number of dropouts for a school district has been 305 per year with a standard deviation of 50. What is the probability that the number of dropouts next year will be a. less than 250? __________ b. less than 300? ________ c. more than 350? _____________ d. more than 400? ____________ e. between 250 and 350? ___________ f. between 300 and 350? ___________ g. between 350 and 375? ___________ ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836 ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

#### Solutions

Chapter
Section
Chapter 5, Problem 5.10P
Textbook Problem
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## S O C The average number of dropouts for a school district has been 305 per year with a standard deviation of 50. What is the probability that the number of dropouts next year will bea. less than 250? __________b. less than 300? ________c. more than 350? _____________d. more than 400? ____________e. between 250 and 350? ___________f. between 300 and 350? ___________g. between 350 and 375? ___________

Expert Solution
To determine

a)

To find:

The probability that the number of students next year will be less than 250.

### Explanation of Solution

Given:

The average number of dropouts for a school district has been 305 per year with a standard deviation of 50.

Description:

The normal curve is symmetrical and its mean is equal to the median. The area below and above the mean is 50% or 0.05.

Formula used:

Let the data values be denoted by Xi.

The formula to calculate the Z score is given by,

Z=XiX¯s

Where, X¯ is the mean and s is the standard deviation of the distribution.

Calculation:

Given that the mean is 305 and standard deviation is 50.

The number of dropout is 250

Expert Solution
To determine

b)

To find:

The probability that the number of students next year will be less than 300.

Expert Solution
To determine

c)

To find:

The probability that the number of students next year will be more than 350.

Expert Solution
To determine

d)

To find:

The probability that the number of students next year will be more than 400.

Expert Solution
To determine

e)

To find:

The probability that the number of students next year will be between 250 and 350.

Expert Solution
To determine

f)

To find:

The probability that the number of students next year will be between 300 and 350.

Expert Solution
To determine

g)

To find:

The probability that the number of students next year will be between 350 and 375.

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