Question

Please fill the blank

Use the 68–95–99.7 Rule to describe this distribution. In a match with 79 ?serves, approximately? 68% of the time she will have between _ and _ good? serves, approximately? 95% of the time she will have between _ and _ good? serves, and approximately? 99.7% of the time she will have between _and good serves. ?(Type integers or decimals. Round to one decimal place as needed. Use ascending? order.)

Answer 1

Suppose probability of good serves is p ( 0 < p < 1)

n = total number of serves = 79

Let X be the random variable which takes the number of good serves

Then E(X) = = n* p = 79p

Variance of X = = n * p * ( 1 - p)

therefore standard deviation of X is = =

Let's use the 68–95–99.7 Rule

In a match with 79 ?serves, approximately? 68% of the time she will have between ( - ) and

( + ) good? serves, approximately? 95% of the time she will have between

( - 2) and ( + 2) good? serves, and approximately? 99.7% of the time she will have between

( - 3) and ( + 3) good serves.

Suppose p = 0.7

Then   = np =79*0.7 = 55.3

and =

Plug these values in the above formula to find the answer.