# Probability Distribution

Section 4.1 Probability Distribution

1. Decide whether the random variable is discrete or continuous.

(References: example 1 page 195, end of section exercises 13 - 20 page 201)

a. The number of bottles of water sold in Florida in August 2008

b. The weight of a wasp in the lab test nest

c. The number of sophomores in a required US History class at Ridgemont High in 2008

d. The weight of a player on the Washington Redskins

e. The number of cars starting in the Darlington 500 in 2008

2. Decide whether the distribution is a probability distribution. If it is not a probability distribution, identify the property that is not satisfied. (References: example 3 and 4 page 197, end of section exercises 25 - 28 page 202 - 203)

x P(x)

1 0.038

2 0.200

3 0.445

4 0.317

3. The number of tennis balls ordered by club members of a country club pro shop has this probability distribution. Balls are packaged in a can of 3. Complete the table shown and find the mean, variance, and standard deviation for the distribution. Round b, c and d to 2 decimal places as needed.

(References: example 5 and 6 page 198 - 199, end of section exercises 29 - 34 page 203)

x P(x) x * P(x) x - mu (x - mu)2 P(x) * (x - mu)2

3 0.04

6 0.18

9 0.36

12 0.36

15 0.06

Sum x * P(x) = Sum P(x) * (x - mu)2 =

a. Complete the table

b. Mean mu

c. Variance σ2

d. Standard Deviation σ

Section 4.2: Binomial Probability

Find the indicated binomial probabilities. Round to the nearest 3 decimal places. (References: example 6 page 212, end of section exercises 15 - 24 page 216 - 217) For part d and e: (References: example 8 page 214)

4. In a local college, 60% of the math majors are women. Fifteen math majors are chosen at random.

a. What is the probability that exactly 5 are women?

b. What is the probability that 5 or less women are selected?

c. What is the probability that 12 women are selected?

d. Find the mean mu

e. Find the variance σ2

5. A multiple choice test has 20 questions with each having 4 possible answers with one correct. Assume a student randomly guesses the answer to every question.

a. What is the probability of getting exactly 9 correct answers?

b. What is the probability of getting less than 9 correct answers?

See attached file.

#### Solution Summary

The solution provides step by step method for the calculation of mean, variance, standard deviation of a probability distribution and binomial probabilities. Formula for the calculation and Interpretations of the results are also included.