Exhibit 8-3
A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph.
-Refer to Exhibit 8-3. The 86.9% confidence interval for $\mu$ is
A)46.500 to 73.500
B)57.735 to 62.265
C)59.131 to 60.869
D)50 to 70

Question

Quizplus · Accepted Answer

To calculate the confidence interval, we use the formula: 
sample mean +/- (critical value) x (standard error), where 
critical value = z-score for desired level of confidence = 1.88 (from z-table)
standard error = standard deviation / sqrt(sample size) = 13.5 / sqrt(81) = 1.5

Plugging in the values, we get: 
60 +/- 1.88 x 1.5
= 60 +/- 2.82

So the 86.9% confidence interval is (60 - 2.82, 60 + 2.82) 
= (57.18, 62.82)

Therefore, the best choice is B) 57.735 to 62.265, which is the closest to the calculated interval.

Exhibit 8-3 a Random Sample of 81 Automobiles Traveling on a Section

Exhibit 8-3
a Random Sample of 81 Automobiles Traveling on a Section