Question

5) 1. The speeds on a stretch of highway are normally distributed with a mean of 68 mph with a standard deviation of 12 mph. The police decide they will only ticket the fastest 1.7% of people driving on the highway. What is the minimum speed you would have to travel in order to get a ticket?

(5) 2. At a job that makes furniture it that rewards efficiency (reduced time to make chairs will result in a bonus). If the average time to make a chair is normally distributed with a mean of 9 hours and a standard deviation of 1.25 hours and you are given a bonus if you can make a chair in the fastest 6.18% of times, what is the maximum time you have to make the chair and still get the bonus?

Answer 1

5) z score corresponding to top 1.7% area = 2.12

Hence,

Minimum speed for ticket = 68 + 2.12*12 = 93.4 mph

6) z score corresponding to bottom 6.18% area = -1.54

Hence,

Maximum time that can be taken to be eligible for bonus

= 9 - 1.54*1.25

= 7.08 hours