Exam P Practice Problem 45 – Heights of Male Students

Problem 45-A

Heights of male students in a large university follow a normal distribution with mean 69 inches and standard deviation 2.8 inches.

Five male students from this university are randomly selected.

What is the probability that the shortest student among the five randomly selected students is taller than 5 feet 5 inches?

Note that one feet = 12 inches.

        \displaystyle A. \ \ \ \ \ \ \ \ \ \ (0.0764)^5

        \displaystyle B. \ \ \ \ \ \ \ \ \ \ 0.0764

        \displaystyle C. \ \ \ \ \ \ \ \ \ \ 0.3279

        \displaystyle D. \ \ \ \ \ \ \ \ \ \ 0.6721

        \displaystyle E. \ \ \ \ \ \ \ \ \ \ 0.9236

The answers are based on this normal table from SOA.

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Problem 45-B

Heights of male students in a large university follow a normal distribution with mean 69 inches and standard deviation 2.8 inches.

Ten male students from this university are randomly selected.

What is the probability that the tallest student among the ten randomly selected students is shorter than 6 feet 2 inches?

Note that one feet = 12 inches.

        \displaystyle A. \ \ \ \ \ \ \ \ \ \ (0.0367)^{10}

        \displaystyle B. \ \ \ \ \ \ \ \ \ \ 0.0367

        \displaystyle C. \ \ \ \ \ \ \ \ \ \ 0.3120

        \displaystyle D. \ \ \ \ \ \ \ \ \ \ 0.6880

        \displaystyle E. \ \ \ \ \ \ \ \ \ \ 0.9633

The answers are based on this normal table from SOA.

_________________________________________________________

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_________________________________________________________

Answers

The answers are based on this normal table from SOA.

_________________________________________________________

\copyright \ 2013

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2 responses

  1. I am struggling with problem 45a. My z value for 5.5ft is -1.36 so
    P(Z>-1.36)=1-P(Z<1.36)=0.0868.
    Do I then subtract this value from 1, and raise it to the fifth power? Please help!!

  2. Please disregard my earlier comment, the Z value should be -1.43, and I figured it out. However, it is still a bit confusing to me when to subtract the probability from 1 then raise the answer to the desired power, or do the converse which is multiply all the probabilities out first then subtract the answer from 1. If you could help me with that, that would be great. Thanks!

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