(6 Pts) The amount of time that customers wait in line during peak hours at one

Question

(6 Pts) The amount of time that customers wait in line during peak hours at one bank is normally distributed with a mean of 14 minutes and a standard deviation of 3 minutes. Using StatCrunch: 2. a) Find the probability that waiting time is between 17 and 19 minutes. b) Find the probability that waiting time is less than 10 minutes. (7 Pts) A study is being planned to estimate the mean number of semester hours taken by students at a college. The population standard deviation is 4.7 hours. How many students should be included in the sample to be 95% confident thatthe sample mean is within 2 semester hours of the population mean, , for all students at this college? 3.

Explanation / Answer

2) mean = 14

Sd = 3

A) P(17 < X < 19) = P((17-mean)/sd < (X - mean) /sd < (19-mean)/sd)

= P(1 < Z < 1.67)

= P(Z < 1.67) - P(Z < 1)

= 0.9525 - 0.8413

= 0.1112

B) P(X < 10) = P((X - mean) /sd < (10-14)/3)

= P(Z < - 1.33)

= 0.0918

2) Margin of error = 2

Z for 95% confidence interval = Z0.975 = 1.96

Margin of error = Z0.975 * sd/sqrt(n)

Or, 2 = 1.96 * 4.7 / sqrt(n)

Or, sqrt (n) = 1.96 * 4.7 / 2

Or, n = 21

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