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 what two amounts? 20) ______ A) $85 and $105 B) $100 and $200 C) $205 and $220 D) $110 and $190

Answer 1

Answer:

D) $110 and $190

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 150

Standard deviation = 20

95% of the monthly food expenditures are between what two amounts?

By the Empirical Rule, within 2 standard deviations of the mean

150 - 2*20 = $110

150 + 2*20 = $190

So the correct answer is:

D) $110 and $190

Answer 2

Answer: D) $110 and $190

Step-by-step explanation:

The Empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

From the information given, the mean is $150 and the standard deviation is $20.

2 standard deviations = 2 × 20 = 40

150 - 40 = $110

150 + 40 = 190

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