Quantitative Reasoning II: Quantitative Research Methods Fall 2016 Name _______________________________ Prof. Ross Flek

Homework Assignment #3 SHOW ALL WORK

#1-3: From the information provided, create the sample space of possible

outcomes, that is, list all of the possible outcomes. (4 points)

1) Flip a coin four times. 2) (4 points) Use the information from question #1 to construct the probability distribution observing the number of tails by completing the table below:

X (The # of Tails) Pr (X) (as a fraction) Pr (X) (as a decimal) Pr (X) (as a %)

3) (4 points) Construct a relative frequency histogram for the above distribution and describe its shape.

#4: Determine whether each of the following is a valid probability distribution. If not, identify the requirement that is not satisfied. (6 points) (a.) (b.) (c.) (d.)

Quantitative Reasoning II: Quantitative Research Methods Fall 2016 Name _______________________________ Prof. Ross Flek

Homework Assignment #3 SHOW ALL WORK

5) (4 points) A die with 12 sides is rolled. What is the probability of rolling a number less than 11?

6) (4 points) Two 6-sided dice, with sides numbered 1 through 6, are rolled, and the top

numbers are observed. What is the probability that the sum of the two top numbers on the dice

will be 4?

7) (4 points) In a certain class of students, there are 12 boys from Wilmette, 3 girls from

Kenilworth, 9 girls from Wilmette, 6 boys from Glencoe, 2 boys from Kenilworth and 6 girls

from Glencoe. If the teacher calls upon a student to answer a question, what is the probability

that the student will be from Kenilworth?

#8-9: Assume that a researcher randomly selects 6 newborn babies and counts the number of girls selected, X. The probabilities corresponding to the 7 possible values of X are summarized in the given table. Answer the question using the table.

X (# of girls) Pr (X) 0 0.015625 1 0.09375 2 0.234375 3 0.3125 4 0.234375 5 0.09375 6 0.015625

8) (4 points) Find the probability of selecting 4 or more girls. 9) (4 points) Find the probability of selecting less than 4 girls. How does this number relate to the answer in the previous question?

Quantitative Reasoning II: Quantitative Research Methods Fall 2016 Name _______________________________ Prof. Ross Flek

Homework Assignment #3 SHOW ALL WORK

10) (2 points) Find the indicated complement. Based on meteorological records, the

probability that it will snow in a certain town on January 1st is 0.148. Find the probability that

in a given year it will not snow on January 1st in that town.

#11: Refer to the table below which displays the results of an observational study

of a large sample of NYC college students. Their gender was recorded as well as

their explicit, or implicit, political affiliations, given a choice of three options plus

a fourth choice for “none 0f the above”. Fill in the missing cells and answer the

questions below. (8 points)

Democrat Republican Independent None of

the above Total

Female (F) 30 42

Male (M) 52 30 28 10 120

Total 60 56 52 300

(a) What percent of all of the participants were Female?

(b) What percent of all of the participants were Democrat?

(c) What percent of all of the participants were Female and chose “None of the above”?

(d) What percent of all participants were Male or chose “None of the above”?

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#12-15: Refer to the table which summarizes the results of testing for a certain,

relatively hard to detect, but not very rare, disease.

Positive Test Result (⊕) Negative Test Result (⊝) Total

Person has the disease (D) 32 28

Person does not have the disease (ND)

8 232

Total

12) What percent of all of the participants have the disease (Pr (D))? (4 points)

13) If one of the results is randomly selected, what is the probability that it is a false positive

(test indicates a positive result when, in fact, the person tested does not have the disease; in

other terms, Pr (⊕/ND))? (4 points)

14) What is the miss rate of this test? That is, what is the probability that the test indicates a

negative result when the person tested does actually have the disease (Pr (⊝/D))? (4 points)

15) What is the Positive Predictive Value of this test? That is, what is the probability that a

person has the disease given the test result was positive (Pr (D/⊕))? (4 points)

Find the indicated probability.

16) A spinner has equal regions numbered 1 through 15. What is the probability that the

spinner will stop on an even number or a multiple of 3? (4 points)

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#17a and #17b: Is Event B dependent or independent of Event A? (Circle the

answer) (4 points)

17(a) A: A mosquito lands on your arm.

B: You get a mosquito bite.

Dependent Independent

17(b) A: A bird lands on your head.

B: The bird lays an egg.

Dependent Independent

Find the indicated probability.

18) In one town, 20% of all voters are Democrats. If two voters are randomly selected for a

survey, assuming their responses are independent, find the probability that they are both

Democrats. (4 points)

19) A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable

and 30% are defective. If three of the products are randomly selected, find the probability that

all of them are acceptable. (4 points)

#20-21: The table below shows the soft drinks preferences of people in three age

groups.

Cola Root Beer Lemon-Lime Under 21 years of age 40 25 20 Between 21 and 40 35 20 30 Over 40 years of age 20 30 35

20) If one of the 255 subjects is randomly selected, find the probability that the person is over

40 years of age. (2 points)

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21) If one of the 255 subjects is randomly selected, find the probability that the person is over

40 and drinks cola. (2 points)

22) If one of the 255 subjects is selected, find the probability that the person is over 40 years of

age given that they drink root beer. (4 points)

#23-24: Find the mean (or, equivalently, the expected value) of the given probability distributions. 23) The random variable x is the number of houses sold by a realtor in a single month at the Brown’s Real Estate office. Its probability distribution is as follows. (4 points)

Houses Sold (X) Probability P(x) 0 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 6 0.11 7 0.21

24) The number of golf balls ordered by customers of a pro shop has the following probability distribution. (4 points)

X P(X) 3 0.14 6 0.11 9 0.36 12 0.29 15 0.10

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25) (4 points) A contractor is considering a sale that promises a profit of $20,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $14,000 with a probability of 0.3. What is the expected profit?

Question # Points Poss. Points Earned #13 4 points #1 4 points #14 4 points #2 4 points #15 4 points #3 4 points #16 4 points #4 6 points #17 4 points #5 4 points #18 4 points #6 4 points #19 4 points #7 4 points #20 2 points #8 4 points #21 2 points #9 4 points #22 4 points

#10 2 points #23 4 points #11 8 points #24 4 points #12 4 points #25 4 points

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