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1. Find the indicated probability. – A die with 6 sides is rolled. What is the probability of rolling a number less than 5? (Points : 5)

4

2/3

1/6

5/6

2. From the information provided, create the sample space of possible outcomes.

Two white mice mate. The male has both a white and a black fur-color gene. The female has only white fur-color genes. The fur color of the offspring depends on the pairs of fur-color genes that they receive. Assume that neither the white nor the black gene dominates. List the possible outcomes. (Points : 5)

WB, BW

WW, BB

WW, WW

WW, BW

3. Find the indicated probability.

If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade? (Points : 5)

25/52

9/26

11/26

1/22

4. Find the indicated probability. Round to the nearest thousandth.

In a batch of 8,000 clock radios 5% are defective. A sample of 14 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire batch will be rejected? (Points : 5)

0.0714

0.512

0.488

0.0500

5. Evaluate the expression.

10P4 (Points : 5)

34

210

5040

6

6. Solve the problem.

There are 6 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? (Points : 5)

20

720

120

216

7. Find the mean of the given probability distribution.

The number of golf balls ordered by customers of a pro shop has the following probability distribution.

x | P(x)

_______

3 | 0.14

6 | 0.05

9 | 0.36

12| 0.35

15| 0.10

(Points : 5)

6.99

7.86

9

9.66

8. 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

x(girls) | P(x) | x(girls) | P(x) | x(girls) | P(x)

_____________________________________

0 | 0.000 | 5 | 10 | 0.061

1 | 0.001 | 6 | 11 | 0.022

2 | 0.006 | 7 | 12 | 0.006

3 | 0.022 | 8 | 13 | 0.001

4 | 0.061 | 9 | 14 | 0.000

Find the probability of selecting 9 or more girls. (Points : 5)

0.001

0.212

0.122

0.061

9. Provide an appropriate response.

A 28-year-old man pays $165 for a one-year life insurance policy with coverage of $140,000. If the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy? (Points : 5)

$84.00

-$164.90

$139,916.00

-$81.00

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

Rolling a single “loaded” die 50 times, keeping track of the “fives” rolled. (Points : 5)

Not binomial: there are too many trials.

Procedure results in a binomial distribution.

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

Not binomial: the trials are not independent.

11. 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. Round to three decimal places.

n = 14, x = 6 , p = 0.5 (Points : 5)

0.238

0.016

0.183

0.275

12. Find the indicated probability. Round to three decimal places.

In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority? (Points : 5)

0.913

0.055

0.985

0.982

13. Find the standard deviation, Sigma, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth.

n = 639; p = 0.7 (Points : 5)

14.85

9.17

11.58

15.70

14. Use the Poisson Distribution to find the indicated probability.

A naturalist leads whale watch trips every morning in March. The number of whales seen has a Poisson distribution with a mean of 1.8. Find the probability that on a randomly selected trip, the number of whales seen is 4. (Points : 5)

0.0723

0.4338

0.1229

0.2892

15. Use the Poisson model to approximate the probability. Round your answer to four decimal places.

The probability that a car will have a flat tire while driving through a certain tunnel is 0.00007. Use the Poisson distribution to approximate the probability that among 10,000 cars passing through this tunnel, at least one will have a flat tire. (Points : 5)

0.5034

0.4966

0.6524

0.3476

0.8558

16. Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.

r = 0.75, n = 9 (Points : 5)

Critical values: r = ±0.666, no significant linear correlation

Critical values: r = 0.666, no significant linear correlation

Critical values: r = -0.666, no significant linear correlation

Critical values: r = ±0.666, significant linear correlation

18. Find the value of the linear correlation coefficient r.

x| 57 53 59 61 53 56 60

———————————–

y| 156 164 163 177 159 175 151

(Points : 5)

-0.054

0.214

0.109

-0.078

19. Use the given data to find the best predicted value of the response variable.

Six pairs of data yield r = 0.789 and the regression equation y(^over the y)=4x – 2. Also, y(- over the y)=19.0 What is the best predicted value of y for x = 5? (Points : 5)

22.0

18.0

18.5

19.0

20. Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

x| 1 3 5 7 9

————————

y| 143 116 100 98 90

Choose A, B, C, or D. (Points : 5)

y^=-150.7+6.8x

y^=150.7-6.8x

y^=140.4-6.2x

y^=-140.4+6.2x

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