The Police Department is investigating the need for a speed camera to be implemented on Hasty Road. A sample of 50 cars passing through that road on a particular day were randomly selected and their speeds recorded. The speed limit on Hasty Road is60 miles per hour (mph). The mean speed for the sample was calculated as43 mph. The standard deviation of the speeds for the sample was calculated as4 mph. The standard deviation for the population of cars driving on Hasty Road is unknown.

a)Select all the techniques that are commonly used to construct a confidence interval for the mean when the population standard deviation () is unknown:

Approximate the population standard deviation () with the sample standard deviation (s)

Replace the sample size (n) withn-1

Approximate the standard normal distribution with the Student's t distribution

Decrease the confidence level to compensate for the increased margin of error

b)Calculate the upper and lower bounds of the 99% confidence interval for the mean speed traveled on Hasty Road. You may find thisStudent's t distribution tableuseful. Give your answers in mph to 2 decimal places.

Upper bound = mph

Lower bound = mph