What is the probability a vacationer will visit at least one of these attractions?
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questions.docx|
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. |
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a. |
What is the probability a vacationer will visit at least one of these attractions? (Round your answer to 2 decimal places.) |
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Probability |
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b. |
What is the probability .35 called? |
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c. |
Are the events mutually exclusive? |
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2.
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P(A1) = .20, P(A2) = .40, and P(A3) = .40. P(B1|A1) = .25. P(B1|A2) = .05, and P(B1|A3) = .10. |
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Use Bayes' theorem to determine P(A3|B1). (Round your answer to 4 decimal places.) |
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P(A3|B1) |
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3.
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Solve the following: |
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a. |
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b. |
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9P 3 |
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c. |
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7C 2 |
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4.
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Which of these variables are discrete and which are continuous random variables? |
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a. |
The number of new accounts established by a salesperson in a year. |
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b. |
The time between customer arrivals to a bank ATM. |
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c. |
The number of customers in Big Nick’s barber shop. |
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d. |
The amount of fuel in your car’s gas tank. |
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e. |
The number of minorities on a jury. |
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f. |
The outside temperature today. |
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5.
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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. |
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a. |
What is the probability that all six arrive within 2 days? (Round your answer to 4 decimal places.) |
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Probability |
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b. |
What is the probability that exactly five arrive within 2 days? (Round your answer to 4 decimal places.) |
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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.) |
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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.) |
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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.) |
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Standard Deviation |
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6.
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In a binomial distribution, n = 12 and π = .60. |
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a. |
Find the probability for x = 5? (Round your answer to 3 decimal places.) |
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Probability |
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b. |
Find the probability for x ≤ 5? (Round your answer to 3 decimal places.) |
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Probability |
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c. |
Find the probability for x ≥ 6? (Round your answer to 3 decimal places.) |
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Probability |
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7.
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A population consists of 15 items, 10 of which are acceptable. |
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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.) |
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Probability |
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8.
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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.) |
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a. |
About what percent of the observations lie between 55 and 65? |
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Percentage of observations |
% |
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b. |
About what percent of the observations lie between 50 and 70? |
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Percentage of observations |
% |
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c. |
About what percent of the observations lie between 45 and 75? |
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Percentage of observations |
% |
9.
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A normal population has a mean of 12.2 and a standard deviation of 2.5. |
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a. |
Compute the z value associated with 14.3. (Round your answer to 2 decimal places.) |
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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.) |
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Proportion |
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c. |
What proportion of the population is less than 10.0? (Round your answer to 4 decimal places.) |
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Proportion |
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10.
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A normal population has a mean of 80.0 and a standard deviation of 14.0. |
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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.) |
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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.) |
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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.) |
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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. |
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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.) |
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Amount |
$ |
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