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 56 minutes. Assume that the arrival times follow a normal distribution.

(a) At what time after the doors open will 88% 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 19% 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

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a.

mean = 180+48 minutes = 228 minutes

stdev = 56 minutes

a. P(X<c) = .88

(c-228)/56 = 1.175

So, c = 56*1.175+228 = 293.8 minutes or 294 minutes

Answer is 294 mins

b.

P(X<c) = .19

(c-228)/56 = -0.8779

c = 56*-.8779+228 = 178.84 minutes. or 179 minutes

Answer is 179 minutes

c.

Yes, they would. why? because we expect the offices to remain closed on Weekend. Therefore people are able to visit the mueseum earlier than during Weekdays, including Fridays