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?A. $205 and $220

B. $85 and $105
C. $100 and $200
D. $110 and $190

Answer 1

The correct answer is D

Step-by-step explanation:

Empirical rule is the rule in statistics, which defined as that for the normal distribution, that is as:

68% of the data fall under one standard deviation of mean.

Data which is 95% lie under the two standard deviations of the mean.

Data (All) which is 99.7% lie under the three standard deviations of the mean.

So, in this case, the sample mean fall under second category, which is as:

= Sample mean ± 2 (Standard deviation)

= $150 ± 2($20)

= $150 ± $40

= $150 + $40 and $150 - $40

= $190 and $110