# Discrete Probability Distributions

1. The probabilities that a customer selects 1, 2, 3, 4 and 5 items at a convenience store are 0.32, 0.12, 0.23, 0.18, and 0.15, respectively. Fill in the probabilities.

Outcome X 1 2 3 4 5

P(X)

2. A study conducted by a TV station showed the number of televisions per household and the corresponding probabilities for each. Find the mean, variance and standard deviation

Number of televisions X 1 2 3 4

Probability P(X) 0.32 0.51 0.12 0.05

Mean:

Variance:

Standard Deviation:

3. A florist determines the probabilities for the number of flower arrangements she delivers each day. Find the mean, variance, and standard deviation for the distribution shown

Number of arrangements X 6 7 8 9 10

Probability P(X) 0.2 0.2 0.3 0.2 0.1

Mean:

Variance:

Standard Deviation:

4. A lottery offers one $1000 prize, one $500 prize, and five $100 prizes. One thousand tickets are sold at $3 each. Find the expectation if a person buys two tickets. Assume that the player's ticket is replaced after each drzw and that the same ticket can win more than one prize. Calculate the expected value.

5. In a Gallup Survey, 90% of the people interviewed were unaware that maintaining a healthy weight could reduce the risk of stroke. If 15 people are selected at random, find the probability that at least 9 are unaware that maintaining a proper weight could reduce the risk of stroke. Show calculations.

6. In a restaurant, a study found that 42% of all patrons smoked. If the seating capacity of the restaurant is 80 people, find the mean, variance, and standard deviation of the number of smokers. About how many seats should be available for smoking customers?

Mean:

Variance:

Standard Deviation:

Answer the question.

7. In a survey, 63% of Americans said they own an answering machine. If 14 Americans are selected at random, find the probability that exactly 9 own an answering machine.. Apply the Binomial Probability Formula, page 247.

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#### Solution Summary

Solutions shows the calculations of probabilities, expected value ,the mean, variance and standard deviation