Question

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 46 minutes. Assume that the arrival times follow a normal distribution. (a) At what time after the doors open will 91% of the people who are coming to the Saturday show have arrived? (Round your answer to the nearest number of minutes.) minutes after doors open (b) At what time after the doors open will only 20% of the people who are coming to the Saturday show have arrived? (Round your answer to the nearest number of minutes.) minutes after doors open (c) 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 1

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 doors opened, and the standard deviation was estimated at about 46 minutes.

A)

At what time after the doors open will 91% of the people.

z-Score for 0.91 is 1.3408

Mean=228,

Standard deviation=46

z=(x-mean)/Sd

1.3408=(x-228)/46

x-228=46*1.3408

x=61.6768+228

x=4 hours 50 minutes.

B)

At what time after the door open will be only 20%

z-score for 0.20 or 20% is

z=-0.8416.

-0.8416=(x-228)/46

x-228=46*(-0.8416)

x=228-38.7136

minutes OR

x=3 hours 9 minutes.

C)

Do you think the probability

Friday,people probability arrive later if they have been working.