Question

Courtney makes 80 % 80%80, percent of the free throws she attempts. She often stays after practice to shoot sets of 10 1010 free throws. Assume that the results of free throws are independent from each other. What are the mean and standard deviation of the number of free throws she makes in each set of 10 1010?

Answer 1

Answer: Mean: 8

Standard Deviation: 1.3

Explanation:

Answer 2

Mean: 8 free throws

Standard Deviation: 1.3 free throws

Explanation:

This is a binomial random variable, so we can use the formula
`ux = np`, where n is the number of trials, and p is the probability. Since we know both of these values, just plug it in for the mean.
`ux = .8*10 = 8`

For the standard deviation, we use the formula σ =
`√(np(1-p))`. Since we know what np is, we can replace those 2, giving us
`√(8(1-p))`. Again, p is our probability, so this gives us our final equation of
`√(8(1-.8))`, which simplifies to
`√(8(.2))`. Using a calculator, we get 1.264, which is 1.3 rounded to the nearest tenth.

Hope this helped :)