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

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

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

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

- 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

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