Discrete and Continuous Probability: Quiz

1. Listed is a series of experiments and associated random variables. In each case, identify the values that the random variable can assume and state whether the random variable is discrete or continuous.

2. The American Housing Survey reported the following data on the number of times that owner-occupied and renter-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months.

Do not round intermediate calculations. Round your answers to two decimal places.

a.  Define a random variable x = number of times that owner-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months and develop a probability distribution for the random variable. (Let x = 4 represent 4 or more times.)

b.  Compute the expected value and variance for x.

c.  Define a random variable y = number of times that renter-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months and develop a probability distribution for the random variable. (Let y = 4 represent 4 or more times.)

d.  Compute the expected value and variance for y.

e.  What observations can you make from a comparison of the number of water supply stoppages reported by owner-occupied units versus renter-occupied units?

The number of times of water supply stoppages in owner-occupied houses is  than in renter-occupied houses, and the variability in the number of times is  for the owner-occupied houses

3. Consider a binomial experiment with n = 20 and p = .70.

If you calculate the binomial probabilities manually, make sure to carry at least 4 decimal digits in your calculations.

a. Compute f(12) (to 4 decimals).  

b. Compute f(16) (to 4 decimals).  

c. Compute P(x > 16) (to 4 decimals).  

d. Compute P(x < 15) (to 4 decimals).  

e. Compute E(x).  

f. Compute Var(x) (to 1 decimal) and  (to 2 decimals).

4. When a new machine is functioning properly, only 9% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found.

a.  Using the  Figure 5.3 , select a tree diagram that shows this problem as a two-trial experiment. Here D: defective; G: not defective.

Choose the Correct option from the above tree diagrams:

b.  How many experimental outcomes result in exactly one defect being found?

c.  Compute the probabilities associated with finding no defects, exactly one defect, and two defects (to 4 decimals).

5. Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.

a. Compute the probability of receiving one call in a 10-minute interval of time.

 (to 4 decimals)

b. Compute the probability of receiving exactly 12 calls in 15 minutes.

 (to 4 decimals)

c. Suppose no calls are currently on hold. If the agent takes 10 minutes to complete the current call, how many callers do you expect to be waiting by that time?

What is the probability that none will be waiting?

 (to 4 decimals)

d. If no calls are currently being processed, what is the probability that the agent can take 3  minutes for a personal time without being interrupted by a call?

 (to 4 decimals)

6. Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 60 employees; the Hawaii plant has 30. A random sample of 10 employees is to be asked to fill out a benefits questionnaire.

Round your answers to four decimal places.

a.  What is the probability that none of the employees in the sample work at the plant in Hawaii?

b.  What is the probability that 1 of the employees in the sample works at the plant in Hawaii?

c.  What is the probability that 2 or more of the employees in the sample work at the plant in Hawaii?

d.  What is the probability that 9 of the employees in the sample work at the plant in Texas?

7. Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let x denote a random number generated using RAND, then x is a continuous random variable with the following probability density function.

a.  Select the probability density function.

b.  What is the probability of generating a random number between 0.25 and 0.75 (to 1 decimals)?

c.  What is the probability of generating a random number with a value less than or equal to 0.3 (to 1 decimals)?

d.  What is the probability of generating a random number with a value greater than 0.6 (to 1 decimals)?

e. Using 50 random numbers given below, compute the mean and standard deviation.

Mean =  (to 6 decimals)

Standard deviation =  (to 6 decimals)

9. During the summer of 2014, Coldstream Country Club in Cincinnati, Ohio collected data on 443 rounds of golf played from its white tees. The data for each golfer's score on the twelfth hole are contained in the DATAfile Coldstream12.

Click on the datafile logo to reference the data.

a.  Construct an empirical discrete probability distribution for the player scores on the twelfth hole. Round probability to 4 decimals.

b.  A par is the score that a good golfer is expected to get for the hole. For hole number 12, par is four. What is the probability of a player scoring less than or equal to par on hole number 12 (to 2 decimals)?

c.  What is the expected score for hole number 12 (to 3 decimals)?

d.  What is the variance for hole number 12 (to 4 decimals)?

e.  What is the standard deviation for hole number 12 (to 4 decimals)?

10. The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 10 seconds.