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# Statistics - All topics - Probability

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Solve the problem.
22)

Find the variance for the given probability distribution.

22)

______
A)

2.46

B)

2.69

C)

7.43

D)

2.63

23)

Find the standard deviation for the given probability distribution.

23)

______
A)

1.71

B)

1.60

C)

2.56

D)

2.45

Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table.

Probabilities of Girls

24)

Find the probability of selecting exactly 8 girls.

24)

______
A)

0.122

B)

0.022

C)

0.183

D)

0.000

25)

Find the probability of selecting 9 or more girls.

25)

______
A)

0.001

B)

0.122

C)

0.212

D)

0.061

26)

Find the probability of selecting 2 or more girls.

26)

______
A)

0.001

B)

0.994

C)

0.006

D)

0.999

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied.
27)

27)

_____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
28)

A contractor is considering a sale that promises a profit of \$ 23,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of \$ 13,000 with a probability of 0.3. What is the expected profit?

28)

______
A)

\$ 12,200

B)

\$ 16,100

C)

\$ 25,200

D)

\$ 10,000

29)

The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one:

Find the expected value of the amount won for one entry if the cost of entering is 73 cents.

29)

______
A)

\$ 0.63

B)

\$ 0.67

C)

\$ 200

D)

\$ 1.29

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
30)

Rolling a single die 19 times, keeping track of the numbers that are rolled.

30)

______
A)

Not binomial: there are more than two outcomes for each trial.
B)

Not binomial: there are too many trials.
C)

Not binomial: the trials are not independent.
D)

Procedure results in a binomial distribution.

31)

Choosing 5 people (without replacement) from a group of 59 people, of which 15 are women, keeping track of the number of men chosen.

31)

______
A)

Not binomial: the trials are not independent.
B)

Procedure results in a binomial distribution.
C)

Not binomial: there are too many trials.
D)

Not binomial: there are more than two outcomes for each trial.

32)

Choosing 3 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with replacement, keeping track of the number of red marbles chosen.

32)

______
A)

Not binomial: there are too many trials.
B)

Procedure results in a binomial distribution.
C)

Not binomial: there are more than two outcomes for each trial.
D)

Not binomial: the trials are not independent.

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.
33)

n = 4, x = 3, p = 1/6

33)

______
A)

0.0039

B)

0.0231

C)

0.0154

D)

0.0116

34)

n = 10, x = 2 , p = 0.5

34)

______
A)

0.0659

B)

0.0571

C)

0.0439

D)

0.2500

35)

n =12, x = 5, p = 0.25

35)

______
A)

0.091

B)

0.027

C)

0.103

D)

0.082

Find the indicated probability.
36)

A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

36)

______
A)

0.945

B)

0.055

C)

0.172

D)

0.117

37)

Find the probability of at least 2 girls in 10 births. Assume that male and female births are equally likely and that the births are independent events.

37)

______
A)

0.011

B)

0.044

C)

0.989

D)

0.945

38)

An airline estimates that 98% of people booked on their flights actually show up. If the airline books 76 people on a flight for which the maximum number is 74, what is the probability that the number of people who show up will exceed the capacity of the plane?

38)

______
A)

0.3340

B)

0.5494

C)

0.8051

D)

0.2154

Find the mean, &#956;, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.
39)

n = 33; p = .2

39)

______
A)

&#956; = 6.9

B)

&#956; = 7.3

C)

&#956; = 6.6

D)

&#956; = 6.1

40)

n = 2466; p = .63

40)

______
A)

&#956; = 1557.3

B)

&#956; = 1545.1

C)

&#956; = 1548.3

D)

&#956; = 1553.6

Find the standard deviation, &#963;, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth.
41)

n = 36; p = .2

41)

______
A)

&#963; = -0.01

B)

&#963; = 6.52

C)

&#963; = 2.40

D)

&#963; = 5.67

42)

n = 2661; p = .63

42)

______
A)

&#963; = 28.18

B)

&#963; = 22.50

C)

&#963; = 29.03

D)

&#963; = 24.91

Use the given values of n and p to find the minimum usual value &#956; - 2&#963; and the maximum usual value &#956; + 2&#963;.
43)

n = 94, p = 0.20

43)

______
A)

Minimum: 11.04; maximum: 26.56

B)

Minimum: -11.28; maximum: 48.88
C)

Minimum: 14.92; maximum: 22.68

D)

Minimum: 26.56; maximum: 11.04

44)

n = 377, p = 2/3
44)

______
A)

Minimum: 269.64; maximum: 233.03

B)

Minimum: 242.18; maximum: 260.49
C)

Minimum: 233.03; maximum: 269.64

D)

Minimum: 238.39; maximum: 264.28

Solve the problem.
45)

According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

45)

______
A)

0.22

B)

2.75

C)

4.00

D)

3.52

46)

A company manufactures batteries in batches of 29 and there is a 3% rate of defects. Find the mean number of defects per batch.

46)

______
A)

28.13

B)

0.841

C)

0.899

D)

0.87

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than &#956; - 2&#963; or greater than &#956; + 2&#963;.
47)

A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 481 consumers who recognize the Dull Computer Company name?

47)

______
A)

Yes

B)

No

48)

According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to "Eyewitness News" at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500 such televisions are randomly selected and checked to determine what is being watched. Would it be unusual to find that 872 of the 2500 televisions are tuned to "Eyewitness News"?

48)

______
A)

Yes

B)

No