Question

The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $150 and the standard deviation is $20. Using the Empirical rule, about 95% of the monthly food expenditures are between which of the following two amounts?

Answer 1

95% of monthly food expenditures are between $110 and $190.

Explanation:

Given : The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $150 and the standard deviation is $20.

To find : Using the Empirical rule, about 95% of the monthly food expenditures are between which of the following two amounts?

Solution :

At 95% of the data is between two standard deviation to left and right of the mean is given by,

To the left side,
`\bar{x}-2\sigma`

To the right side,
`\bar{x}+2\sigma`

We have given,

The sample mean
`\bar{x}=\$150`

The standard deviation
`\sigma=\$20`

Substitute in the formula,

`\bar{x}-2\sigma`

`=150-2(20)`

`=150-40`

`=110`

`\bar{x}+2\sigma`

`=150+2(20)`

`=150+40`

`=190`

Therefore, 95% of monthly food expenditures are between $110 and $190.