# 1. value: 10.00 points It is claimed that Proactine, a new medicine for acne

1.

value:

**10.00 points**

It is claimed that Proactine, a new medicine for acne, is 75 percent effective. It is applied to the affected area of a group of 15 people. Calculate the probability for the following (Round your answers to 3 decimal places): |

(a) |
All 15 will show significant improvement |

Probability |

(b) |
Fewer than 9 of 15 will show significant improvement |

Probability |

(c) |
That 12 or more people will show significant improvement |

Probability |

2.

value:

**10.00 points**

A study of the attendance at the University of Alabama’s basketball games revealed that the distribution of attendance is normally distributed with a mean of 9,600 and a standard deviation of 1,800. |

(a) |
What is the probability a particular game has an attendance of 13,500 or more? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) |

Probability |

(b) |
What percent of the games have an attendance between 8,000 and 11,500? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) |

Probability |

(c) |
Ten percent of the games have an attendance of how many or less? |

Attendance | |

3.

value:

**10.00 points**

The distribution of the number of school-age children per family in the Whitehall Estates area of Boise, Idaho, is: |

Number of children | 0 | 1 | 2 | 3 | 4 |

Percent of families | 25 | 30 | 40 | 3 | 2 |

(a) |
Determine the mean and standard deviation of the number of school-age children per family in Whitehall Estates. (Round your answers to 2 decimal places.) |

Mean | |

Standard deviation | |

(b) |
A new school is planned in Whitehall Estates. An estimate of the number of school-age children is needed. There are 500 family units. How many children would you estimate? |

Children |

Some additional information is needed about only the families having children. |

(c-1) |
Convert the preceding distribution to one for families with children. (Round your answers to 5 decimal places.) |

Number of
Children ( |
Probability
given Children |

1 | |

2 | |

3 | |

4 | |

(c-2) |
What is the mean number of children among families that have children? (Round your answer to 2 decimal places.) |

Mean |

4.

value:

**10.00 points**

First National Bank thoroughly investigates its applicants for small home-improvement loans. Its default record is very impressive: The probability that a homeowner will default is only .005. The bank has approved 400 small home-improvement loans. Assuming the Poisson probability distribution applies to this problem: |

(a) |
What is the probability that no homeowners out of the 400 will default? (Round your answer to 4 decimal places.) |

Probability |

(b) |
How many of the 400 are expected not to default? |

Expected value |

(c) |
What is the probability that 3 or more homeowners will default on their small home-improvement loans?(Round your answer to 4 decimal places.) |

Probability |

5.

value:

**10.00 points**

Daniel-James Insurance Company will insure an offshore Mobil Oil production platform against weather losses for one year. The president of Daniel-James estimates the following losses for that platform (in millions of dollars) with the accompanying probabilities: |

Amount of Loss
($ millions) |
Probability
of Loss |

0 | .98 |

40 | .016 |

300 | .004 |

Click here for the Excel Data File |

(a) |
What is the expected amount Daniel-James will have to pay to Mobil in claims? (Enter your answer in millions to 2 decimal places. Omit the “$” sign in your response.) |

Expected amount | $ million |

(b) |
What is the likelihood that Daniel-James will actually lose less than the expected amount? (Round your answer to 2 decimal places.) |

Probability |

(c) |
Given that Daniel-James suffers a loss, what is the likelihood that it is for $300 million? (Round your answer to 2 decimal places.) |

Probability |

(d) |
Daniel-James has set the annual premium at $2.0 million. Does that seem like a fair premium? Will it cover its risk? |

(Click to select)YesNo |

6.

value:

**10.00 points**

The manager of Tee Shirt Emporium reports that the mean number of shirts sold per week is 1,170 with a standard deviation of 315. The distribution of sales follows the normal distribution. |

What is the likelihood of selecting a sample of 25 weeks and finding the sample mean to be 1,100 or less?(Round z value to 2 decimal places and final answer to 4 decimal places.) |

Probability |

7.

value:

**10.00 points**

The manager of Tee Shirt Emporium reports that the mean number of shirts sold per week is 1,210, with a standard deviation of 325. The distribution of sales follows the normal distribution. |

What is the likelihood of selecting a sample of 25 weeks and finding the sample mean to be 1,100 or less?(Round z value to 2 decimal places and final answer to 4 decimal places.) |

Probability |

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