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Exhibition Shows: Inverse Normal Distribution

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

(a) At what time after the doors open will 90% of the people who are coming to the Saturday show have arrived?

(b) At what time after the doors open will only 15% of the people who are coming to the Saturday show have arrived?

(c) Do you think the probability distribution of arrival times for Friday might be different from the distribution of arrival times for Saturday? Explain.

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