Please Help! Answers would be great. If possible explain how to do in excel as w

Question

Please Help! Answers would be great. If possible explain how to do in excel as well.

These problems must be solved using an Excel spreadsheet and formulas. Make sure your work is displayed in a clear manner. Submit your work as directed. The time required to sail the Mobile Bay Yacht Club Dauphin Island Race is normally distributed, with a mean of 2 hours and a standard deviation of 30 minutes. What percentage of the boats complete the run in one hour or less? What percentage of boats will take between two and a half hours to three hours to finish the race? If the maximum time limit is three and a half hours, what percentage will not have finished the race when the time expires?

Explanation / Answer

we need to convert the hours into minutes

therefore mean = 2hrs= 120

standard dev = 30

a) p(x<60) =

For x = 60, the z-value z = (60 - 120) / 30 = -2

Hence P(x < 60) = P(z < -2) = [area to the left of -2] = 0.0228 = 2.28%

b)p(150<x<180) =

For x = 150 , z = (150 - 120) / 30 = 1 and for x = 180, z = (180 - 120) / 30 = 2

Hence P(150 < x < 180) = P(1 < z <2) = [area to the left of z = 2] - [area to the left of 1]

= 0.9772 - 0.8413 = 0.1359 = 13.59%

c)p(x>210) =

For x = 210, z = (210 - 120) / 30 = 3

Hence P(x > 210) = P(z > 3) = [total area] - [area to the left of 3]

= 1 - 0.9987 = 0.0013 = 0.13%

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