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    Probability Distribution

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    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.

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    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.

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