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 93% 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 17% 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.

a) 305; b) 179; c) Yes

Step-by-step explanation:

We use z scores for these questions.  The formula for a z score is

The mean, μ, is 3 hours and 48 minutes; this is 3(60)+48 = 180+48 = 228 minutes.  The standard deviation, σ, is 52.

For part a,

We look 93%, or 0.93, up in the cells of a z table.  The closest we can get to this value is 0.9306, which corresponds to a z score of 1.48:

1.48 = (X-228)/52

Multiply both sides by 52:

52(1.48) = ((X-228)/52)*52

76.96 = X-228

Add 228 to each side:

76.96+228 = X-228+228

304.96 = X

This rounds to 305 minutes.

For part b,

We look 17%, or 0.17, up in the cells of a z table.  The closest we can get to this value is 0.1685, which corresponds to a z score of -0.95:

-0.95 = (X-228)/52

multiply both sides by 52:

52(-0.95) = ((X-228)/52)*52

-49.4 = X-228

Add 228 to each side:

-49.4+228 = X-228+228

178.6 = X

This rounds to 179 minutes.

For part c,

Yes, the distribution might be different for Friday than for Saturday.  People that work Monday through Friday might not get off work until Friday evening, but might be off all day on Saturday.  This might mean they can get to the theater sooner on Saturday than they can on Friday.

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