Finite Math 8.1

QUESTION 1

Suppose a probability distribution of a random variable X is represented by the accompanying histogram. Shade that part of the histogram whose area gives the probability .

a.b.c.d.e.

1 points  

QUESTION 2

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous.

X = The number of times an accountant takes the CPA examination before passing
a.0 ≤ x < 24; continuous

b.0 ≤ x < ∞; continuous

c.Any integer; infinite discrete

d.Any positive integer; infinite continuous

e.Any positive integer; infinite discrete

1 points  

QUESTION 3

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

The area of a histogram associated with a probability distribution is a number between 0 and 1.

 a.False. The area is exactly equal to one.

b.True. This follows from the definition.

1 points  

QUESTION 4

Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are cast. Find P ( X = 5 ).​

a.

b.

c.

d.

1 points  

QUESTION 5

An examination consisting of ten true-or-false questions was taken by a class of 100 students. The probability distribution of the random variable X, where X denotes the number of questions answered correctly by a randomly chosen student, is represented by the accompanying histogram. The rectangle with base centered on the number 8 is missing. What should be the height of this rectangle?​

​a.0.4

b.0.25

c.0.2

d.0.35

1 points  

QUESTION 6

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous.​
X = The distance a commuter travels to work
​a.. The random variable is finite discrete.

b.. The random variable is infinite discrete.

c.. The random variable is continuous.

1 points  

QUESTION 7

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous.​
X = The number of defective watches in a sample of four watches.

​a.{0,1,2,3,4}; The random variable is finite discrete

b.X may assume the values of any positive integer. The random variable is continuous.

c.X may assume the values of any positive integer. The random variable is infinite discrete.

d.{0,1,2,3,4}; The random variable is infinite discrete

1 points  

QUESTION 8

Suppose a probability distribution of a random variable X is represented by the accompanying histogram. Shade that part of the histogram whose area gives the probability .​

​a.

b.

c.​

d.

e.

1 points  

QUESTION 9

The accompanying data were obtained in a study conducted by the manager of one supermarket. In this study the number of customers waiting in line at the express checkout at the beginning of each 3-min interval between 9 A.M. and 12 noon on Saturday was observed.

Customers012345678910Frequency of Occurrence312812797533
Find the probability distribution of the random variable X, where X denotes the number of customers observed waiting in line. Draw the histogram representing the probability distribution.

a.x          0    1     2     3     4
P(X = x)  0.05 0.017 0.033 0.133 0.2
x         5     6    7     8    9     10
P(X = x)  0.117 0.15 0.107 0.05 0.083 0.05

b.x           0    1     2     3     4
P(X = x)   0.05 0.017 0.033 0.153 0.2
x          5     6    7     8     9    10
P(X = x)   0.107 0.15 0.117 0.083 0.05 0.05

c.x          0    1     2     3     4
P(X = x)  0.05 0.017 0.033 0.133 0.2
x         5     6    7     8     9    10
P(X = x)  0.117 0.15 0.117 0.083 0.05 0.05

1 points  

QUESTION 10

After the private screening of a new television pilot, audience members were asked to rate the new show on a scale of 1 to 10 (10 being the highest rating). From a group of 140 people, the accompanying responses were obtained.
Rating12345678910Frequency of Occurrence2431322182630175​
​
Let the random variable X denote the rating given to the show by a randomly chosen audience member. Find the probability distribution associated with these data. Round answer to the nearest thousandth.

x2345678P(X = x)​​​​​​​

a.​x12345678910P(X = x)​​​​​​​​​​​

b.​x12345678910P(X = x)​​​​​​​​​​​

c.​x12345678910P(X = x)​​​​​​​​​​​

d.​x12345678910P(X = x)​​​​​​​​​​​

e.​x12345678910P(X = x)​​​​​​​​​

Two

QUESTION 1

The management of the Cambridge Company has projected the sales of its products (in millions of dollars) for the upcoming year, with the associated probabilities shown in the following table:

SalesProbability
What does the management expect the sales to be next year?
a.18.7

b.15.34

c.28.98

d.29.61

e.32.34

1 points  

QUESTION 2

The management of MultiVision, a cable TV company, intends to submit a bid for the cable television rights in one of two cities, A or B. If the company obtains the rights to city A, the probability of which is 0.3, the estimated profit over the next 10 yr is $10 million; if the company obtains the rights to city B, the probability of which is 0.4, the estimated profit over the next 10 yr is $7 million. The cost of submitting a bid for rights in city A is $300,000 and that of city B is $300,000.​
By comparing the expected profits for each venture, determine whether the company should bid for the rights in city A or city B.
​a.City A

b.City B

1 points  

QUESTION 3

In European roulette the wheel is divided into 37 compartments numbered 1 through 36 and 0. (In American roulette there are 38 compartments numbered 1 through 36, 0, and 00.) Find the expected value of the winnings on a $3 bet placed on red in European roulette. Round your answer to the nearest cent.

a.$0.08%

b.$0.03%

c.- $0.03%

d.- $0.08%

1 points  

QUESTION 4

Based on past experience, the manager of the VideoRama Store has compiled the following table, which gives the probabilities that a customer who enters the VideoRama Store will buy 0, 1, 2, 3, or 4 videocassettes. How many videocassettes can a customer entering this store be expected to buy?

Video- cassettes01234Probability0.420.370.130.040.04

a.E = 0.56

b.E = 0.91

c.E = 0.86

d.E = 0.66

1 points  

QUESTION 5

Find the expected value of a random variable X having the following probability distribution:

x012345P(X = x)

a.E( X) = 2.3125

b.E( X) = 2.1875

c.E( X) = 2.3825

d.E( X) = 1.0975

1 points  

QUESTION 6

If a player placed a $8 bet on red and a $5 bet on black in a single play in American roulette, what would be the expected value of his winnings? Round your answer to the nearest cent.

a. cents

b. cents

c. cents

d. cents

e. cents

1 points  

QUESTION 7

During the first year at a university that uses a 4-point grading system, a freshman took ten 3-credit courses and received one A, three Bs, two Cs, and four Ds.

Compute this student’s grade point average.

Let the random variable X denote the number of points corresponding to a given letter grade. Find the probability distribution of the random variable X and compute E( X), the expected value of X.

a. 2.1;
x 1 2 3 4
P (X = x) 1 3 2 4
E(X) = 2.1

b. 2.9;
x 1 2 3 4
P (X = x) 0.4 0.2 0.3 0.1
E(X) = 2.9

c. 2.9;
x 1 2 3 4
P (X = x) 0.1 0.3 0.2 0.4
E(X) = 2.9

d. 2.1;
x 1 2 3 4
P (X = x) 0.4 0.2 0.3 0.1
E(X) = 2.1

1 points  

QUESTION 8

A woman purchased a $10,000, 1-year term-life insurance policy for $150. Assuming that the probability that she will live another year is 0.993, find the company’s expected gain.

a.E = $90

b.E = $100

c.E = $140

d.E = $80

1 points  

QUESTION 9

Bob, the proprietor of Midland Lumber, feels that the odds in favor of a business deal going through are 7 to 6. What is the (subjective) probability that this deal will not materialize?

a.0.4622

b.0.4615

c.0.4647

d.0.4460

1 points  

QUESTION 10

A buyer for Discount Fashions, an outlet for women’s apparel, is considering buying a batch of clothing for $61,000. She estimates that the company will be able to sell it for $80,000, $75,000, or $70,000 with probabilities of 0.20, 0.40, and 0.40, respectively.

Based on these estimates, what will be the company’s expected gross profit?

a.$10,400

b.$23,400

c.$13,000

d.$7,800

e.$15,600

1 points