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

A National Park Service survey of visitors to the Rocky Mountain region revealed that 50% visit Yellowstone Park, 40% visit the Tetons, and 35% visit both.

a.

What is the probability a vacationer will visit at least one of these attractions? (Round your answer to 2 decimal places.)

  Probability

c.

Are the events mutually exclusive?

P(A₁) = .20, P(A₂) = .40, and P(A₃) = .40.  P(B₁|A₁) = .25. P(B₁|A₂) = .05, and P(B₁|A₃) = .10.

Use Bayes' theorem to determine P(A₃|B₁). (Round your answer to 4 decimal places.)

  P(A₃|B₁)

b.

 The time between customer arrivals to a bank ATM.

c.

 The number of customers in Big Nick’s barber shop.

d.

 The amount of fuel in your car’s gas tank.

e.

 The number of minorities on a jury.

f.

 The outside temperature today.

The U.S. Postal Service reports 95% of first-class mail within the same city is delivered within 2 days of the time of mailing. Six letters are randomly sent to different locations.

a.

What is the probability that all six arrive within 2 days? (Round your answer to 4 decimal places.)

  Probability

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b.

What is the probability that exactly five arrive within 2 days? (Round your answer to 4 decimal places.)

  Probability

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c.

Find the mean number of letters that will arrive within 2 days. (Round your answer to 1 decimal place.)

  Number of letters

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d-1.

Compute the variance of the number that will arrive within 2 days. (Round your answer to 3 decimal places.)

  Variance

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d-2.

Compute the standard deviation of the number that will arrive within 2 days. (Round your answer to 4 decimal places.)

  Standard Deviation

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In a binomial distribution, n = 12 and π = .60.

a.

Find the probability for x = 5? (Round your answer to 3 decimal places.)

  Probability

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b.

Find the probability for x ≤ 5? (Round your answer to 3 decimal places.)

  Probability

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c.

Find the probability for x ≥ 6? (Round your answer to 3 decimal places.)

  Probability

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A population consists of 15 items, 10 of which are acceptable.

In a sample of four items, what is the probability that exactly three are acceptable? Assume the samples are drawn without replacement. (Round your answer to 4 decimal places.)

  Probability

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The mean of a normal probability distribution is 60; the standard deviation is 5. (Round your answers to 2 decimal places.)

a.

About what percent of the observations lie between 55 and 65?

  Percentage of observations

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b.

About what percent of the observations lie between 50 and 70?

  Percentage of observations

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c.

About what percent of the observations lie between 45 and 75?

  Percentage of observations

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A normal population has a mean of 12.2 and a standard deviation of 2.5.

a.

 Compute the z value associated with 14.3. (Round your answer to 2 decimal places.)

  Z

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b.

 What proportion of the population is between 12.2 and 14.3? (Round your answer to 4 decimal places.)

  Proportion

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c.

 What proportion of the population is less than 10.0? (Round your answer to 4 decimal places.)

  Proportion

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A normal population has a mean of 80.0 and a standard deviation of 14.0.

a.

Compute the probability of a value between 75.0 and 90.0. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)

  Probability

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b.

Compute the probability of a value of 75.0 or less. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)

  Probability

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c.

Compute the probability of a value between 55.0 and 70.0. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)

  Probability

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For the most recent year available, the mean annual cost to attend a private university in the United States was $26,889. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,500.

Ninety-five percent of all students at private universities pay less than what amount? (Round z value to 2 decimal places and your final answer to the nearest whole number.)

  Amount

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