SOLUTION: Most exhibition shows open in the morning and close in the late evening. A study of Saturday arrival times showed that the average arrival time was 3 hours and 48 minutes after the

Algebra ->  Probability-and-statistics -> SOLUTION: Most exhibition shows open in the morning and close in the late evening. A study of Saturday arrival times showed that the average arrival time was 3 hours and 48 minutes after the      Log On


   

Question 1088425: Most exhibition shows open in the morning and close in the late evening. A study of Saturday arrival times showed that the average arrival time was 3 hours and 48 minutes after the doors opened, and the standard deviation was estimated at about 59 minutes. Assume that the arrival times follow a normal distribution.
(a) At what time after the doors open will 94% of the people who are coming to the Saturday show have arrived?
At what time after the doors open will only 16% of the people who are coming to the Saturday show have arrived? (Round your answer to the nearest number of minutes.)
Do you think the probability distribution of arrival times for Friday might be different from the distribution of arrival times for Saturday? Explain your answer.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
z for 0.94 or 94th percentile is +1.555.
228 minutes is mean
59 minutes is sd
z=(x-mean)/sd
1.555=(x-228)/59
91.745=x-228
x=319.75 minutes or 5h19.75m
================
16% is z=-0.95
-0.96=(x-228)/59
-56.64=x-228
x=171.36 minutes of 2h51.36m
Friday, people probably arrive later if they have been working.