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Probability Study Questions

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A study by the National Park Service revealed that 50 percent of vacationers going to the Rocky Mountain region visit Yellowstone Park, 40 percent visit the Tetons, and 35 percent visit both.

a. What is the probability a vacationer will visit at least one of these attractions?

b. What is the probability .35 called?

c. Are the events mutually exclusive? Explain.

Probability

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A normal distribution has a mean of 50 and a standard deviation of 4.
a-compute the probability of a value between 44.0 and 55.0.
b-compute the probability of a value greater than 55.0.
c-compute the probability of a value between 52.0 and 55.0

Probability distribution

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If the probability of getting caught copying someone else’s exam is .1, find the probability of not getting caught in three attempts. Assume independence.

Probability

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1.Sixyy nine percent of adults favor gun licensing in general. Choose one adult at random. What is the probability that the selected adult doesn’t believe in gun licensing?

2.In a recent year, of the 1,184,000 bachelor’s degrees conferred, 233,000 were in the field of business, 125,000 were in the social sciences, and 106,000 were in education. If one degree is selected at random, find the following probabilities.

a. That the degree was awarded in education.
b. That the degree was not awarded in business.

3.In a survey, 16 percent of American children said they use flattery to get their parents to buy them things. If a child is selected at random, find the probability that the child said he or she does not use parental flattery.

4.The source of federal government revenue for a specific year is

50% from individual income taxes
32% from social insurance payroll taxes
10% from corporate income taxes
3% from excise taxes
5% other

If revenue is selected at random, what is the probability that it comes from individual or corporate income taxes?

5.At a used book sale, 100 books are adult books and 160 books are children’s books. Seventy of the adult books are nonfiction while 60 of the children’s books are nonfiction. If a book is selected at random, find the probability of selecting the following

a. fiction

b. not a children’s nonfiction

c. an adult book or a children’s nonfiction

6. This distribution represents the length of time a patient spends in a hospital
Days Frequency
0-3 2
4-7 15
8-11 8
12-15 6
16+ 9
If a patient is selected, find these probabilities

a.the patient spends 3 days or fewer in the hospital
b.the patient spends fewer than 8 days in the hospital
c.the patient spends 16 or more days in the hospital
d.the patient spends a maximum of 11 days in the hospital

7. If one half of Americans believe that the federal government should take primary responsibility for eliminating poverty, find the probability that three randomly selected Americans will agree that it is the federal governments responsibility to eliminate poverty.

8. A circuit to run a model railroad has eight switches. Two are defective. If a person selects two switches at random and tests them, find the probability that the second one is defective, given that the first one is defective.

9. A lot of portable radios contains 15 good radios and 3 defective ones. If two are selected and tested, find the probability that at least one will be defective.

10. A medication is 75% effective against a bacterial infection. Find the probability that if 12 people take the medication, at least one person’s infection will not improve.

Discrete Probability Distributions

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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.

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.