Question

Given that the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet, what is the probability he throws it no less than 55 feet?

Answer 1

P(X>55)=0.16

Explanation:

We want to find the probability that an athlete throws the hammer no less than 55 feet given that the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet.

We know that 55 is 1 stand deviation above the mean which is 50.

By the empirical rule, 68% of the distribution is within 1 standard deviation of the mean.

In this case only one standard deviation above the mean will give 34% .

So the probability that he throws the hammer less than 55 feet is 0.5+0.34=0.84

The probability that he throws it no less than 55 feet is 1-0.84=0.16