Question

Suppose that the average and standard deviation of the fine for speeding on a particular highway are 111.12 and 13.04, respectively. Calculate an interval that is symmetric around the mean such that it contains approximately 68% of fines. Assume that the fine amount has a normal distribution. 1) (124.16, 98.08) 2) (111.12, 13.04) 3) (98.08, 124.16) 4) (85.04, 137.2) 5) (137.2, 85.04)

Answer 1

Answer:

3) (98.08, 124.16)

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 = 111.12

Standard deviation = 13.04

Calculate an interval that is symmetric around the mean such that it contains approximately 68% of fines.

68% of the fines are within 1 standard deviation of the mean speed. So

From 111.12 - 13.04 = 98.08 to 111.12 + 13.04 = 124.16

The interval notation in the smallest value before the highest value.

So the correct answer is:

3) (98.08, 124.16)