Question

A certain group of welfare recipients receives snap benefits of $110 per week with a standard deviation of $20. If a random sample of 25 people is taken, what is the probability their mean benefit will be greater than $118 per week?

Answer 1

Given:

Benefits = $110 per week

Standard deviation = $20

Number of people = 25

To find:

The probability their mean benefit will be greater than $118 per week

Solution:

Find z score,

Z score = ( Mean benefits - benefits ) / Standard deviation √ Number of people

( 118 - 110 ) / 20 √25

8 / ( 20 / 5)

8 / 4

2

Z score = 2

Using the z table, it is found that the z score of 2 approximately covers an area if 47.72 %

Hence,

Adding the 50 % on the left,

We get,

97.72 %

Hence,  the probability their mean benefit will be greater than $118 per week is 97.72 %