Answer to Question #244872 in Statistics and Probability for s12

Question

A group of automotive engineers decided to conduct a study of its school buses and found that for 30 buses, the average stopping distance of buses traveling 50 miles per hour was 251 feet. The standard deviation of the population was 3.2 feet. Find the 99% confidence interval of the mean. 

a.      Margin of error

 

b.     Confidence interval

 

 

c.      Would a bus stopping at a distance of 249.5 feet be smaller than average? Explain.

 

Answer 1

$\sigma=3.2 \\ n=30 \\ \bar{x}=251$

The value of z at 99% confidence level is 2.576.

The standard error is

$SE = \frac{\sigma}{\sqrt{n}} \\ = \frac{3.2}{\sqrt{30}}=0.5843$

a. The margin of error is

$ME = Z \times SE \\ = 2.576 \times 0.5843 = 1.50$

b. The 99% confidence interval is

$\bar{x}±ME = 251 ± 1.5 \\ =(249.5, 252.5)$

c. A bus stopping at a distance of 249.5 feet is NOT smaller than average, because this value lies in confidence interval.