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

Answer:

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

Step-by-step 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.