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problem1.)  Exit polling has been a controversial practice in recent elections, since early release of the resulting information appears to affect whether or not those who have not yet voted will do so.  Suppose that 83% of all registered NC voters favour banning the release of information from exit polls in presidential elections until after the polls in NC close.  A random sample of 75 NC voters is to be selected.

a.)  What is the probability which no more than 65 voters favour the ban?
b.)  What is the probability which at least 56 voters favour the ban?
c.)  What is the mean value of number of voters who favour the ban? 
d.)  What is standard deviation of number of voters who favour the ban?   
e.)  What is probability which is exactly 52 voters favour the ban? 

problem2.)  On the basis of past knowledge an insurance salesperson knows that the number of long-term health care insurance policies sold per week by the company is a random variable x with the following probability distribution.

    X        p(x)
    0        0.245
    1        0.143
    2        0.125
    3        0.096
    4        0.078
    5        0.064
    6        0.039
    7        0.029
    8        0.181

Assume that a week is randomly selected. Find
a.)  p(x=3)    b.) p(x 4)    c.) p(x     d.) p(1


problem3.)  The scores on Algebra test have a mean of 73 and the standard deviation of 7.  If 85% of the students must have a passing score, what is that score? 

problem4.)   The average diameter of sand dollars on a certain island is 4.25 centimetres with a standard deviation of 0.70 centimetres. If 16 sand dollars are selected at random for a collection, find the probability that the average diameter of those sand dollars is more than 4.13 centimetres. (Hint:  Use the Central Limit Theorem) 

problem5.)  At a large department store, the average number of years of employment for a cashier is 4.2 with a standard deviation of 2.1 years, and the distribution is approximately normal. If an employee is picked at random, what is the probability that employee has worked at the store for over 5 years?

problem6.)  A sample of 500 racing cars showed that 75 of them cost over $700,000. What is the 95% confidence interval for the true proportion of racing cars that cost over $700,000?  Give an interpretation for this confidence interval. 

problem7.)   In a study of 10 insurance sales reps from a certain large city, the average age of the group was 46.6 and the standard deviation was 3.8 years.  Find the 95% confidence interval of the population mean age of all insurance sales reps in that city.  Give an interpretation for this confidence interval. 

problem8.)
  A medical researcher wishes to determine the percentage of females who take vitamins.  He wishes to be 99% confident that the estimate is within 2 percentage points of the true proportion.  A recent study of 250 females showed that 45% took vitamins.  How large should the sample size be? 

problem9.) 
A state executive claims that the average number of acres in western PA state park is less than 2000 acres.  A random sample of five parks is selected, and the number of acres is given below.  With α = 0.01, is there enough evidence to support the claim?
959    1187    493    6249    541 

problem10.) 
A telephone company representative estimates that 45% of its customers have call waiting service.  To test this hypothesis, she selected a sample of 100 customers and found that 37% had call waiting.  With α = 0.01, is there enough evidence to reject the claim?

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
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