Discuss the following:
Q1. A specialty bookstore concentrates mainly on used books. Paperbacks are $1.00 each, and hardcover books are $3.50. Of the 50 books sold last Tuesday morning, 40 were paperback and the rest were hardcover. What was the weighted mean price of a book?
Q2. A major cost factor in the purchase of a home is the monthly loan payment. There are many Websites where prospective home buyers can shop the interest rates and determine their monthly payment. Capital Bank of Virginia is considering offering home loans on the Web. Before making a final decision, a sample of recent loans is selected and the monthly payment noted. The information is organized into the following frequency distribution.
Monthly Mortgage Payment Number of Homeowners
$ 100 up to $ 500 1
500 up to 900 9
900 up to 1,300 11
1,300 up to 1,700 23
1,700 up to 2,100 11
2,100 up to 2,500 4
2,500 up to 2,900 1
Total 60
a. Determine the mean monthly payment.
b. Determine the median monthly payment.
Q3. Listed below are the salaries for the New York Yankees for the year 2000. The salary information is reported in millions of dollars.
$9.86 $9.50 $8.25 $6.25 $6.00 $5.95
5.25 5.00 4.33 4.30 4.25 3.40
3.13 2.02 2.00 1.90 1.85 1.82
0.80 0.38 0.35 0.35 0.20 0.20
0.20 0.20 0.20 0.20 0.20
a. Determine the mean, median, and the standard deviation.
b. Determine the coefficient of skewness using Pearsonâ??s method.
c. Determine the coefficient of skewness using the software method.
Q4. A new sports car model has defective brakes 15 percent of the time and a defective steering mechanism 5 percent of the time. Let's assume (and hope) that these problems occur independently. If one or the other of these problems is present, the car is called a 'lemon'. If both of these problems are present, the car is a 'hazard'. Your instructor purchased one of these cars yesterday. What is the probability it is:
a. A lemon?
b. A hazard?
Q5. Reynolds Construction Company has agreed not to erect all ook-alike' homes in a new subdivision. Five exterior designs are offered to potential home buyers. The builder has standardized three interior plans that can be incorporated in any of the five exteriors. How many different ways can the exterior and interior plans be offered to potential home buyers?
Q6. A new chewing gum has been developed that is helpful to those who want to stop smoking. If 60 percent of those people chewing the gum are successful in stopping smoking, what is the probability that in a group of four smokers using the gum at least one quits smoking?
Q7. There are four people being considered for the position of chief executive officer of Dalton Enterprises.
Three of the applicants are over 60 years of age. Two are female, of which only one is over 60.
a. What is the probability that a candidate is over 60 and female?
b. Given that the candidate is male, what is the probability he is less than 60?
c. Given that the person is over 60, what is the probability the person is female?