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Calculating the Variance of a Discrete Random Variable

  • 1.

    At a fair, tickets are drawn to win or lose money. Here is the probability distribution that represents the situation.

    X = amount won -$4-$1$0$2$5
    P(X=x) 0.10.20.40.20.1

    Find the variance of the amount won.

    Answers:

    • $5.57

    • $2.24

    • $2.36

    • $5.01

  • 2.

    The following table summarizes the results of a study of the number of children in families.

    X = number of children 01234
    P(X=x) 0.30.20.250.20.05

    What is the variance in the number of children? Choose the closest answer.

    Answers:

    • 1.24

    • 2.25

    • 2.5

    • 1.55

  • 3.

    The following table summarizes the results of a study of the number of shoes a group of students own.

    X = number of shoes 3891014
    P(X=x) 0.30.20.290.20.01

    Find the variance of the number of shoes. Select the best answer.

    Answers:

    • 2.89

    • 15.7

    • 3.96

    • 8.39

  • 4.

    One new board came is based on spinning a wheel to find out how many spaces a piece moves forward (or back) on a turn. This is the probability distribution of the outcomes of the wheel.

    X = spaces moved -2-1025
    P(X=x) 0.250.20.30.20.05

    Find the variance of the situation. Choose the closest answer.

    Answers:

    • 7.7

    • 3.25

    • 1.80

    • 2.77

  • 5.

    Some friends are taking part in a small lottery game where they can either win or lose money. Here is a summary of the outcomes.

    X = amount of money -$2.50$0.5$1$2
    P(X=x) 0.20.150.30.20.15

    Find the variance of the amount of money. Pick the best answer.

    Answers:

    • $2.10

    • $1.45

    • $1.68

    • $2.82

  • 6.

    At the front of the store is a cart with irregular shirts. The shirts are either missing buttons or have too many. Andy reaches into the cart and grabs a shirt at random. This table summarizes the probabilities for each incorrect number of buttons.

    X = buttons -5-3-201
    P(X=x) 0.150.150.30.20.2

    Which of the the values below is the variance of the number of buttons?

    Answers:

    • 1.98

    • 2.39

    • 5.70

    • 3.94

  • 7.

    When playing a football game, there are points assigned to each play. One one position, there can be negative or positive points. This is the probability distribution of the points:

    X = points -10367
    P(X=x) 0.050.250.40.250.05

    Find the variance of the situation. Choose the closest answer.

    Answers:

    • 12.5

    • 6.1

    • 3.54

    • 2.47

  • 8.

    The following table summarizes the results of a study of the number of pets live in American homes.

    X = number of pets 01234
    P(X=x) 0.250.250.280.20.02

    Find the variance of the number of children. Choose the closest answer.

    Answers:

    • 1.13

    • 1.58

    • 2.5

    • 1.27

  • 9.

    One new board came is based on spinning a wheel to find out how many spaces a piece moves forward (or back) on a turn. This is the probability distribution of the outcomes of the wheel.

    X = spaces moved -2-10235
    P(X=x) 0.150.20.30.20.050.1

    Calculate the variance for this distribution. Choose the closest answer.

    Answers:

    • 4.25

    • 6.97

    • 2.12

    • 2.64

  • 10.

    When hiring a new employee, a company researched the salaries of their current employees. Here is a distribution of salaries (in thousands).

    X = salary 1015305075
    P(X=x) 0.150.20.30.20.15

    Compute the variance of the salaries. Select the best answer.

    Answers:

    • 21.59

    • 466.19

    • 26.79

    • 717.50

  • 11.

    Over the holiday, Joe's family plays a lottery type game where people either lose or win money. Here is the probability distribution of the lottery.

    X = amount of money -$2-$1$1$2$7
    P(X=x) 0.20.150.30.20.15

    Find the variance of the amount of money. Pick the best answer.

    Answers:

    • $12.30

    • $3.51

    • $7.96

    • $2.77

  • 12.

    One new board came is based on rolling a weighted four sided die to find out how many spaces a piece moves forward (or back) on a turn. This is the probability distribution of the outcomes of the wheel.

    X = spaces moved -2023
    P(X=x) 0.30.20.30.2

    What is the variance of spaces moved?

    Answers:

    • 3.84

    • 1.96

    • 2.22

    • 4.92

  • 13.

    Anna has several values of coins in her purse and pulls out one randomly. Here is a table of the probability distribution related to the amounts possible.

    X = coin amount 151025
    P(X=x) 0.150.250.350.25

    Compute the variance of the amounts, and select the best answer below.

    Answers:

    • 73.33

    • 110.25

    • 10.50

    • 8.56

  • 14.

    A large family is having a dinner where each person is asked to bring at least one dish. To be fair, Grandma spins a wheel for each person in order to figure out the number of dishes to bring. Here is a summary of the possible outcomes.

    X = number of dishes 1234
    P(X=x) 0.250.250.30.2

    Calculate the variance in number of dishes and choose the closest answer below.

    Answers:

    • 1.15

    • 1.67

    • 1.29

    • 1.07

  • 15.

    Each section of a dart board shows a different point amounts that a player can win or lose. Based on the sections of the board, the table below represents the probability distribution.

    X = points amount -3-1014
    P(X=x) 0.150.250.30.26.04

    Find the variance in points and select the closest value below.

    Answers:

    • 1.56

    • 6.70

    • 2.59

    • 2.42

  • 16.

    Calculate the variance of the probability distribution given below.

    x 0 1 2
    P(x) 0.3 0.5 0.2

    Answers:

    • 0.59

    • 0.49

    • 0.45

    • 0.55

  • 17.

    Using the probability distribution determine the variance.

    x 1 2 3 4
    P(x) 0.3 0.2 0.2 0.3

    Answers:

    • 1.65

    • 1.75

    • 1.45

    • 1.55

  • 18.

    Identify the correct variance of the following probability distribution.

    x 0 1 2 3
    P(x) 0.18 0.32 0.25 0.25

    Answers:

    • 1.11

    • 1.4

    • 2.11

    • 2.4

  • 19.

    Which of the following options represents the variance of the given probability distribution?

    x 1 2 3 4 5
    P(x) 0.15 0.15 0.2 0.4 0.1

    Answers:

    • 1.63

    • 1.57

    • 1.53

    • 1.67

  • 20.

    Evaluate the variance of the probability distribution given below.

    x 1 2 3 4
    P(x) 0.15 0.25 0.25 0.35

    Answers:

    • 1.19

    • 1.16

    • 1.2

    • 1.13

  • 21.

    Use the probability distribution to determine the variance.

    x 0 1 2
    P(x) 0.1 0.45 0.45

    Answers:

    • 0.42

    • 0.43

    • 0.41

    • 0.44

  • 22.

    Choose the correct variance of the following probability distribution.

    x 0 1 2 3 4 5
    P(x) 0.1 0.1 0.3 0.15 0.3 0.05

    Answers:

    • 1.84

    • 1.94

    • 1.64

    • 1.74

  • 23.

    Which of the following choices represents the variance of the given probability distribution?

    x 0 1 2 3
    P(x) 0.25 0.25 0.3 0.2

    Answers:

    • 1.13

    • 1.17

    • 1.15

    • 1.19

  • 24.

    Find the variance of the probability distribution given below.

    x 1 2 3 4
    P(x) 0.1 0.3 0.2 0.4

    Answers:

    • 1.09

    • 1.07

    • 1.03

    • 1.05

  • 25.

    With the help of the probability distribution determine the variance.

    x 1 2 3 4 5
    P(x) 0.2 0.3 0.2 0.1 0.2

    Answers:

    • 1.76

    • 1.66

    • 1.86

    • 1.96

  • 26.

    Identify the correct variance of the following probability distribution.

    x 0 1 2
    P(x) 0.15 0.35 0.5

    Answers:

    • 0.53

    • 0.83

    • 0.73

    • 0.63

  • 27.

    Which of the following options represents the variance of the given probability distribution?

    x 1 2 3 4
    P(x) 0.25 0.25 0.1 0.4

    Answers:

    • 1.23

    • 1.43

    • 1.53

    • 1.33

  • 28.

    Calculate the variance of the probability distribution given below.

    x 0 1 2 3
    P(x) 0.7 0.1 0.1 0.1

    Answers:

    • 1.07

    • 1.06

    • 1.09

    • 1.04

  • 29.

    Using the probability distribution determine the variance.

    x 1 2 3 4 5
    P(x) 0.08 0.12 0.3 0.15 0.35

    Answers:

    • 1.53

    • 1.63

    • 1.67

    • 1.57

  • 30.

    Select the correct variance of the following probability distribution.

    x 1 2 3 4
    P(x) 0.5 0.2 0.15 0.15

    Answers:

    • 1.15

    • 1.25

    • 1.45

    • 1.35

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