A non-audition dance group will accept the first n male and the first n female a

ID: 3318580 • Letter: A

Question

A non-audition dance group will accept the first n male and the first n female applicants.

Assume that people apply independently.

The distribution of the heights of male applicants is normal with a mean of 70 inches and a standard deviation of 4 inches.

The distribution of the heights of female applicants is normal with a mean of 66 inches and a standard deviation of 3 inches.

Male and female applicants are paired randomly to be dance partners.

What is the probability that a male applicant is more than 3 inches taller than his female dance partner?

here expected mean difference between male and female partner height =70-66 =4

and std deviation =(42+32)1/2 =5

therefore probability that a male applicant is more than 3 inches taller than his female dance partner

=P(X>3) =P(Z>(3-4)/5)=P(Z>-0.2)=1-P(Z<-0.2)=1-0.4207 =0.5793

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