Chapter 5.2 Page 250 # 7, 9, 11, 13, 15, 17, 19, 21, 25 ...

Chapter 5.2 Page 250 # 7, 9, 11, 13, 15, 17, 19, 21, 25, 27

For exercises 6 through 11, determine whether the distribution represents a probability distribution. If it does not, state why.

7. X 3 6 8 12 P(x) 0.3 0.5 0.7 -0.8

No, we cannot have negative numbers, and P(x) does not equal 1.

9. X 12345 P(x)

10

= = 1, yes 1.

10

Each P(x) is between 0 and 1. p(x) 10 1. 10

11. X

5 10 15

P(x) 1.2 0.3 0.5

2 1, No, not equal to 1. 1. P(x) = 1.2 is not between 0 and 1, 2. p(x) 2 1

For Exercises 12 through 18, state whether the variable is discrete or continuous.

13. The number of cheeseburgers a fast-food restaurant serves each day. Discrete

15. The weight of a Siberian tiger. Continuous

17. The number of mathematics majors in your school.

Discrete

For Exercises 19 through 26, construct a probability distribution for the data and draw a graph for the distribution.

19. Medical tests the probabilities that a patient will have 0, 1, 2, or 3 medical tests performed on

entering a hospital are 6 , 5 , 3 , and 1 respectively. 15 15 15 15

X P(X) 0 6/15 1 5/15 2 3/15 3 1/15

21. Defective Parts The probabilities of a machine manufacturing 0, 1, 2, 3, 4, or 5 defective parts in one day are 0.75, 0.17, 0.04, 0.025, 0.01 and 0.005, respectively.

X P(X) 0 0.75 1 0.17 2 0.04 3 0.025 4 0.01 5 0.005

Probability

0.8

0.750

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0 0

Defective Parts

0.170

1

0.040

0.025

2

3

De fe c t iv e pa r t s

0.010

4

0.005

5

25. Surgical Operations The probabilities that a surgeon operates on 3, 4, 5, 6, or 7 patients in any one day are 0.15, 0.20, 0.25, 0.20, and 0.20, respectively.

X P(X) 3 0.15 4 0.20 5 0.25 6 0.20 7 0.20

27. Selecting a Monetary Bill A box contains two $1 bills, three $5 bills, one $10 bill, and three $20 bills. Construct a probability distribution for the data.

X P(X) $1 2/9

$5 3/9 $10 1/9 $20 3/9

Chapter 5.3 Page 259 Number's 3, 5, 6, 7, 11, 12, 13, 14, 15, 18

3. Number of Credit Cards A bank vice president feels that each savings account customer has, on average, three credit cards. The following distribution represents the number of credit cards people won. Find the mean, variance, and standard deviation. Is the vice president correct?

Number of

Credit

Cards X

0

1

2

3

4

Probability 0.18 0.44 0.27 0.08 0.03 P(X)

Mean: X P( X ) 0 0.18 1 0.44 2 0.27 3 0.08 4 0.03 1.34 Variance 2 X 2 P( X ) 2

02 0.18 12 0.44 22 0.27 32 0.08 42 0.03 1.342 2.72 1.7956 0.9 Standard deviation 0.9 1

No, the vice president is not correct. On average, each person has about one credit card.

5. Public Speaking a public speaker computes the probabilities for the number of speeches she gives each week. Compute the mean, variance, and standard deviation of the distribution shown.

Number of speeches X 0 1 2 3 4 5

Probability P(x)

0.06 0.42 0.22 0.12 0.15 0.03

x x2 P(x) XP(x) x2 P (x)

0 0 0.06 0

0

1 1 0.42 0.42 0.42

2 4 0.22 0.44 0.88

3 9 0.12 0.36 1.08

4 16 0.15 0.60 2.4

5 25 0.03 0.15 0.75

Sum =

1.97 4.53

Mean: X P( X ) 0 0.06 1 0.42 2 0.22 3 0.12 4 0.15 5 0.03 1.97

Variance 2 X 2 P( X ) 2 4.53 1.972 1.649

Standard deviation = 1.649 1.28

6. Number of Bedrooms a recent survey by an insurance company showed the following probabilities for the number of bedrooms in each insured home. Find the mean, variance, and standard deviation for the distribution.

Number of bedrooms X 2 3 4 5

Probability P(x)

0.3 0.4 0.2 0.1

x x2 P(x) XP(x) x2 P (x)

2 4 0.3 0.6 1.2

3 9 0.4 1.2 3.6

4 16 0.2 0.8 3.2

5 25 0.1 0.5 2.5

Sum =

3.1 10.5

Mean: X P(X ) 3.1

Variance 2 X 2 P(X ) 2 10.5 3.12 0.89

Standard deviation = 0.89 0.9

7. Commercials during children's TV programs a concerned parents group determined the number of commercials shown in each of five children's programs over a period of time. Find the mean, variance, and standard deviation shown.

Number of commercials X 5 6 7 8 9

Probability P(x)

0.2 0.25 0.38 0.10 0.07

x x2 P(x) XP(x) x2 P (x)

5 25 0.2 1

5

6 36 7 49 8 72 9 81 Sum =

0.25 1.5 0.38 2.66 0.10 0.8 0.07 0.63

6.59

9 18.62 6.4 5.67 44.69

2 44.69 (6.59)2 44.69 43.43 1.26 1.26 1.123 1.12 , 6.59

11. Insurance an insurance company insures a person's antique coin collection worth $20,000 for an annual premium of $300. If the company figures that the probability of the collection being stolen is 0.002, what will be the company's expected profit?

P (of being stolen) = 0.002

Worth=20,000

P (of not being stolen) = 0.998

premium=300=20,000-300=19,700

x Profit 300 Loss -19,700 Sum =

P(x) 0.998 0.002

x p(x) 299.4 -39.4 260

Expected profit is $260.0.

12. Job Bids a landscape contractor bids on jobs where he can make $3000 profit. The probabilities of getting one, two, three, or four jobs per month are shown.

Number of jobs X 1 2 3 4 Probability P(x) 0.2 0.3 0.4 0.1

Find the contractor's expected profit per month.

Mean: X P( X ) 1(0.2) 2(0.3) 3(0.4) 4(0.1) 2.4

Per month the contractor's expected profit is 2.4($3000) = $7200

13. Rolling Dice if a person rolls doubles when he tosses two dice, he wins $5. For the game to be fair, how much should the person pay to play the game?

Win

Gain x

$5

Probability P(x) 1/6

X P( X ) 5(1 / 6) 0.83 Therefore, he has to pay $0.83 for the game to be fair.

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