Name:    Probability Distributions

Multiple Choice
Identify the choice that best completes the statement or answers the question.

Using the formula above, answer the questions that follow.

1.

The number of trials is
 a. n b. C c. r d. P e. Q f. n-r g. Not listed on its own

2.

The number of failures is
 a. n b. C c. r d. P e. Q f. n-r g. Not listed on its own

3.

The probability of success is
 a. n b. C c. r d. P e. Q f. n-r g. Not listed on its own

4.

The number of successes is
 a. n b. C c. r d. P e. Q f. n-r g. Not listed on its own

5.

The number of ways “n” trials can yield “r” number of successes is
 a. n b. C c. r d. P e. Q f. n-r g. Not listed on its own

6.

This formula is used to calculate a specific probability for  which probability distribution?
 a. Uniform b. Binonmial c. Geometric d. Hypergeometric e. Normal (symetrical)

7.

The expected number of successes for the formula above is:
 a. Q ÷ P b. X • P(x) c. r • (n/a) d. n • P e. Indeterminable

8.

Which of the following statements is false?
 a. Geometric trials contiue until there is a success, then stop. b. In binomial probability distributions, trials can be categorized as a success or a failure. c. The probability of success is constant for all distributions d. Essentially, the calculation of the expected number of successes is the same for hypergeometric and binomial distributions.

9.

The formula above is expected value for a hypergeometric distribution. The probability of success is
 a. r b. a c. n d. a ÷ n

10.

Why does the binomial formula contain the combination formula nCr or trialsCsuccesses?
 a. To count the number of successes in “n” number of trials b. To calculate the probability of success c. To count of the number of different ways a series of trials could produced the desired number of successes d. To count the number of orders in which the success can occur in a set of trials.

11.

The number of trials required for to calculate P(x) must be known outset for which of the following distributions?
 a. Binomical b. Geometric c. Hypergeometric d. All of these e. None of these

12.

Of all the probability formulas, which one is cumulative and returns a value that measures the probability of “r” number of successes or less?
 a. The binomial probability formula b. The geometric probability formula c. The hypergeometric probability formula d. All of the above e. None of the above

13.

For the formula above, why is Q raised to the power of n-1
 a. This is the number of failures for a geometric probability distribution b. This is one less trial than the total “n”, to account for the final trial that must be a success c. All the above are correct d. All of the above are false

Use the graph above to answer the following questions.

14.

Based on the graph of the binomial distribution, how many trials were there?
 a. 10 b. 8 c. 4 d. It’s impossible to estimate

15.

Based on the graph of the binomial distribution, what was the probability of success?
 a. 10% b. 38% c. 5% d. 20% e. 80%

16.

What is the probability of achieving two or more successes in ten trials?
 a. ~19% b. ~28% c. ~72% d. None of these is correct

17.

To calculate the precise value of the probability of achieving two or more successes in ten trials (as shown in this graph), you would use 10C2(0.10)2(0.90)8.
 a. True b. False c. Can’t be determined

Use the graphs below to answer the following questions. Click the image to pop out the image.

18.

Which graph is for a geometric probability distribution?
 a. Graph A b. Graph B c. Graph C d. Graph D

19.

For which distribution is the probability of success 50%?
 a. Graph A b. Graph B c. Graph C d. Graph D

20.

Which two graphs have P and (1-P) respectively, as their probabilities of success? In other words, which graph has P as the probability of success, and which other graph has the complement of P as its probability of success?
 a. A and B b. A and C c. A and D d. B and C e. B and D f. D and C

21.

Which graph is for a binomial probability distribution?
 a. Graph A b. Graph B c. Graph A and B d. Graph B and C e. All of them f. All but graph A

22.

What is the probability of success for the geometric probability distribution?
 a. 30% b. 70% c. 50% d. 15% e. Can’t be determined

Multiple Response
Identify one or more choices that best complete the statement or answer the question.

Use the formulas below to answer the questions that follow. Click the image to pop out the formulas for easier viewing.

23.

Which of the formula(s) above would you use to solve the following problem:

A casino has created the following game involing two dice. The rolls and payouts are listed. What is the most you would pay to play this game?

 Die Roll Payout 2 or 12 \$20 6 \$5 7 \$4 8 \$5 doubles \$10 All else \$0

 a. Formula A b. Formula B c. Formula C d. Formula D e. Formula E f. Formula F g. Formula G h. Formula H

24.

Which of the formula(s) above would you use to solve the following problem:

A casino has created the following game involing two dice. How many times would you expect to win this game if you played ten times?

 Die Roll Payout 2 or 12 \$20 6 \$5 7 \$4 8 \$5 doubles \$10 All else \$0

 a. Formula A b. Formula B c. Formula C d. Formula D e. Formula E f. Formula F g. Formula G h. Formula H

25.

Which of the formula(s) above would you use to solve the following problem:

If your crush tells you that 95% of everybody you ask out will reject you (your crush isn’t very nice), how many people are you going to have to ask out to get a date to the prom?

 a. Formula A b. Formula B c. Formula C d. Formula D e. Formula E f. Formula F g. Formula G h. Formula H

26.

Which of the formula(s) above would you use to solve the following problem:

If you have a 50% chance of passing an exam in a course you’ve never attended, and a university degree has 40 half-year courses, what are the chances of you earning your degree without ever spending a day in school? (Assume passing the exam earns you the credit).

 a. Formula A b. Formula B c. Formula C d. Formula D e. Formula E f. Formula F g. Formula G h. Formula H

27.

Which of the formula(s) above would you use to solve the following problem:

If you have a 50% chance of passing an exam in a course you’ve never attended, and a university degree has 40 half-year courses, how many final exams would you expect to pass without ever spending a day in school?

 a. Formula A b. Formula B c. Formula C d. Formula D e. Formula E f. Formula F g. Formula G h. Formula H

28.

Which of the formula(s) above would you use to solve the following problem:

The engineering and quality control department of a manufacturing firm is testing for defects. The particular product is a package containing an assortment of fasteners that customers can buy. They contain three different types of screws and bolts (10 small, 20 medium, and 5 large). If past performance indicates a defect rate of 1%, 0.4%, and 0.5% per fastener, respectively, what should this particular product sample's acceptable defect rate be?
 a. Formula A b. Formula B c. Formula C d. Formula D e. Formula E f. Formula F g. Formula G h. Formula H

29.

Which of the formula(s) above would you use to solve the following problem:

The engineering and quality control department of a manufacturing firm is testing for defects. The particular product is a package containing an equal assortment of fasteners that customers can buy. They contain three different types of screws and bolts (10 small, 20 medium, and5 large). Past performance indicates a defect rate of 1%, 0.4%, and 0.5% per fastener, respectively. If a bin containing all the fasteners prior packaging is tested, and it contains 100 small fasteners, 150 medium ones, and 75 large ones,

a) What is the probability in a sample of 9 fasteners, that you will have exactly 3 of each kind?

b) How many of each kind would you expect?

c) What should the defect rate be in the sample that is most likely to be drawn?
 a. Formula A b. Formula B c. Formula C d. Formula D e. Formula E f. Formula F g. Formula G h. Formula H

30.

Which of the formula(s) above would you use to solve the following problem:

The engineering and quality control department of a manufacturing firm is testing for defects. The particular product is a package containing an assortment of fasteners that customers can buy. They contain three different types of screws and bolts (10 small, 20 medium, and 5 large). Past performance indicates a defect rate of 1%, 0.4%, and 0.5% per fastener, respectively. If a giant bin containing all the fasteners prior packaging is tested, and it contains 10,000 small fasteners, 15,000 medium ones, and 7,500 large ones,

a) If you tested 100 small fasterns one at a time, what are the chances you’d never find a defect until the very end?

b) How many should you find in 100 samples?
 a. Formula A b. Formula B c. Formula C d. Formula D e. Formula E f. Formula F g. Formula G h. Formula H

31.

Which of the formula(s) above would you use to solve the following problem:

You are conducting a marketing survey for a family sedan. To avoid statistical discrepancy and sampling bias, you need to randomly sample 1,001 people who drive Toyotas and are a parent in a family of four (two adults and two children), which is only 4.7% of the total population. If in your experience you know that only 20% of people comply with a telephone survey request, how many people do you need to call to complete this task?
 a. Formula A b. Formula B c. Formula C d. Formula D e. Formula E f. Formula F g. Formula G h. Formula H