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

| November 18, 2015

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 (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  

 

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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