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

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

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

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 (X)

Probability given Children P(X)

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

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

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?

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

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