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Probability: Boy Scout Troop Weight

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The weights of the 100 boys in the Boy Scout Troop 829 are normally distributed with a mean of 170 pounds and a standard deviation of 5 pounds.

a. What is the probability that a boy picked at random weighs less than 165 pounds?

b. How many boys would you expect to weigh between 161 and 173 pounds?

c. Find the 96th percentile.

d. Find the cutoff values which represents the middle 80% of their weight.

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Solution Summary

This solution provides concise, easy-to-understand calculations and explanations for finding probability, percentile, and cutoff values to answer the problem related to Boy Scout Troop weights.

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Let X denote the weights of the 100 boys in the Boy Scout Troop 829. Then X is normally distributed with a mean mu=170 pounds and a standard deviation sigma=5 pounds.

a) P(X<165) = P(z < (165-170)/5) = P(z < -1.00) = 0.1587
b) P(161<X<173) = ...

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