Question

A certain volleyball player makes a successful serve 80% of the time. Assume that each serve is independent of the others. If she serves 7 times, use the information on her serve and the MINTAB results to answer questions 1-3:

Cumulative Distribution Function

n = 7 and p = 0.8

x P( X <= x )

0      0.00001

1      0.00037

2      0.00467

3      0.03334

4      0.14803

5      0.42328

6      0.79028

7      1.00000

1. Describe the random variable, X.
   1. Define random Variable

2. Describe random variable (distribution, measure of center and spread)

2. What is the mean number of successful serves, if she serves 7 times?

3. Compute the standard deviation of the number of successful serves, if she serves 7 times.

                      

Answer 1

a) here we interested in number of times a volleyball player makes a successful serve.

So Let X is number of successful serve of volleyball player.

X is a random variable it's possible values 0,1,2,....,7.

b) The X follows binomial distribution with n = 7 and p = 0.80

The measure of center of X is mean = n * p = 7 * 0.80

Mean = 5.6

The measure of spreads are variance and standard deviation

Variance = ² =  n * p *(1-p) = 7*0.80*0.20 = 1.12

Standard deviation = = n*p*(1-p) = 1.06

Mean number of successful serve = 5.6

Standard deviation of number of successful serve = 1.06