These problems must be solved using an Excel spreadsheet and formulas. 1.The tim

Question

These problems must be solved using an Excel spreadsheet and formulas. 1.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 .

a) What percentage of the boats comple te the run in one hour or less ?

b) What percentage of boats will take between two and a half hours to three hours to finish the race ?

c) If the maximum time limit is three and a half hours, what percentage will not have finish ed the race when the time expires?

Explanation / Answer

a)For X=1, z=(x-mu)/sigma=(1-2)/0.5=-2

P(X<=1)=P(z<-2)=0.0228

The required percentage is 2.228%

b)For X=2.5, z=(2.5-2)/0.5=1

For X=3, z=(3-2)/0.5=2

P(2.5<X<3)=P(X<3)-P(X<2.5)

=P(z<2)-P(z<1)=0.9772-0.8413=0.1359

The required percentage is 13.59%

c)For X=3.5, z=(3.5-2)/0.5=3

P(X>3.5)=1-P(X<3.5)=1-P(z<3)=1-0.9987=0.0013

The required percentage is 0.13%

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