A large company must hire a new president. The Board of Directors prepares a list of five candidates, all of whom are equally qualified. Two of these candidates are members of a minority group. To avoid bias in the selection of the candidate, the company decides to select the president by lottery. |

a. |
What is the probability one of the minority candidates is hired? (Round your answer to 1 decimal place.) |

Probability |

b. |
Which concept of probability did you use to make this estimate? |

The chair of the board of directors says, “There is a 50% chance this company will earn a profit, a 30% chance it will break even, and a 20% chance it will lose money next quarter.” |

a. |
Use an addition rule to find the probability the company will not lose money next quarter. (Round your answer to 2 decimal places.) |

= |

b. |
Use the complement rule to find the probability it will not lose money next quarter. (Round your answer to 2 decimal places.) |

= |

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 |

b. |
What is the probability .35 called? |

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) |

Solve the following: |

a. |

b. |

9P 3 | |

c. |

7C 2 |

Which of these variables are discrete and which are continuous random variables? |

a. | The number of new accounts established by a salesperson in a year. | |

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 |

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

Probability |

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

Number of letters |

d-1. |
Compute the variance of the number that will arrive within 2 days. (Round your answer to 3 decimal places.) |

Variance |

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

Standard Deviation |

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

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

Probability |

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

Probability |

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

Probability |

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 |

According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts. |

a. |
What is the mean amount spent on insurance? |

Mean | $ |

b. |
What is the standard deviation of the amount spent? (Round your answer to 2 decimal places.) |

Standard deviation | $ |

c. |
If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year? (Round your answer to 4 decimal places.) |

Probability |

d. |
What is the probability a family spends more than $3,000 per year? (Round your answer to 4 decimal places.) |

Probability |

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 | % |

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

Percentage of observations | % |

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

Percentage of observations | % |

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 |

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

Proportion |

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

Proportion |

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 |

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 |

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 |

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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