Complaints about poor service led the Department of Motor Vehicles to investigate wait times at a local branch.

Question

Complaints about poor service led the Department of Motor Vehicles to investigate wait times at a local branch. During one week, DMV employees randomly asked 50 people leaving this branch how long they had to wait in line. The selected people waited an average of 65.9 minutes, with a standard deviation of 6.3 minutes. Find a 99% confidence interval for the mean wait time at this DMV branch during that week. 

a. 63.6 < 𝜇 < 68.2 b. 66.6 < 𝜇 < 68.4 c. 63.6 < 𝜇 < 68.4

Answer 1

Our equation is:

Confidence Interval = sample mean +/- critical value * (sample standard deviation / square root of n)

From the word problem we know:

Sample mean = 65.9

Sample standard deviation = 6.3

N (sample size) = 50

Critical value for 99% = 2.576

Our math should look as follows:

Confidence Interval = 65.9 +/- 2.576*(6.3 / sqrt of 50)

= 65.9 +/- 2.576*(6.3 / 7.07)

= 65.9 +/- 2.576*.891

= 65.9 +/- 2.295

= 65.9 - 2.295 = 63.605 or 63.6

= 65.9 + 2.295 = 68.195 or 68.2

So our answer is [63.6, 68.2] for the 99% confidence interval, so option A is the correct answer.