Formulas:

p(x) = pxqn-x

1. (9 points) Fifteen percent of airport Dollar Rent A Car operations are off site, while the rest are inside airport terminals. What is the probability that at a random sample of 12 airports, more than 2 will be off site?

   Binomial, n = 12, p = .15, Find P(X > 2)

   Use the binomial table

   P(X > 2) = 1 - P(X < 2) = 1 - 0.7358 = 0.2642

2. (9 points) Cadillac claims that 82% of the paint jobs on its cars are right after the first pass on the assembly line. What is the probability that of 10 randomly selected cars from the assembly line, 7 of them will have good paint jobs after the first pass?

   Binomial, n = 10, p = .82, Find P(X = 7)

   Use the binomial formula

   = 120 x 0.00000016 x 0.614 = 0.00012

3. (6 points) Let z be a standard normal random variable. Find P(0.7 < z < 1.42).

   

   P(0.7 < z < 1.42) = P(0 < z < 1.42) - P(0 < 0.7) = 0.4222 - 0.2580 = 0.1642

   
   
4. (8 points) If employee's salaries are uniformly distributed between $20,000 and $80,000, what is the probability of a particular employee having a salary above $34,000?

   
   

   P(34000 < X < 80000) = = 46000 / 60000 = 0.767

   
   
5. (8 points) Suppose a certain task requires workers an average of 2.4 minutes to complete with standard deviation 0.6 minutes. If the time required is normally distributed, what is the probability that a certain worker will require more than 2.0 minutes to complete the task?

   Find P(x > 2.0) where m = 2.4 and s = 0.6

   x = 2.0 corresponds to z = = -0.67

   P(x > 2.0) = P(z > -0.67) = 0.5 + P(0 < z < 0.67) = 0.5 + 0.2486 = 0.7486

   
6. (9 points) Suppose that a manufacturer's sheet metal has a mean thickness of 0.20 inches with standard deviation 0.021 inches. What is the probability that a random sample of 40 sheets will have mean thickness 0.191 inches or less?

   Find P( < 0.191) where m = 0.20 and s = 0.021

   = 0.191 corresponds to z = = -2.71

   P( < 0.191) = P(z < -2.71) = 0.5 - P(0 < z < 2.71) = 0.5 - 0.4966 = 0.0034

   
7. (9 points) In 1989, Baskin Robbins offered frozen yogurt in 36% of its stores. If a random sample of 50 Baskin Robbins stores were selected in that year, what is the probability that more than 40% of them offered frozen yogurt?

   Find P( > 0.40) where p = 0.36 and n = 50

   = 0.40 corresponds to

   P( > 0.40) = P(z > 0.59) = 0.5 - 0.2224 = 0.2776

   
8. (10 points) A sample of 10 three year old Corvettes sold for an average price of $22,000 with standard deviation $1200. Construct a 95% confidence interval for the average price of all three year old Corvettes.

   
   Use t since n < 30 and s is unknown.

   

   We are 95% certain that the average price for all three year Corvettes is between 21,142 and 22,858.

   
   
9. (10 points) A sample of 80 computer chips from an assembly line showed a 30% defect rate. Construct a 95% confidence interval for the portion of all computer chips that are defective.

   
   Binomial, n = 80 = 0.30.
   Check for normality: n p = (80)(0.3) = 24 > 5, n q = (80)(0.7) = 56 > 5.
   

   

   We are 95% certain that the portion of all computer chips that are defective is between 0.1996 and 0.4004.

   
   
10. (10 points) A utilities company found that a sample of 100 delinquent accounts yields an average amount owed of $131 with standard deviation $16. Construct a 90% confidence interval for the average amount owed for all delinquent accounts.

    
    Use z since n > 30.
    

    We are 90% certain that the average amount owed for all delinquent accounts is between 128.368 and 133.632.

    
    

11. (10 points) How large a sample would be needed to estimate the average price of a meal in Washington, D.C, to within $4 with 95% confidence if s = $5.30?

    Find n so that

    

    Round up to n = 7.