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Historically, the star basketball player of the local team has a 45% success rate at sinking baskets. He seems to be on a 'cold streak', missing 8 in a row. You know about his past history, so you bet your friend that he's due, since his overall probability of getting a basket is high compared to his recent performance. Is this a correct conclusion? (1pt)

Select one:

a. No, because he's obviously on a cold streak

b. No, because the odds do not change

c. Yes, because he needs to make up some misses to get his percentage today back up to 45%

d. Yes, with his past performance, his cold streak can't continue much longer.

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In a sample, there are 200 red shirts, 150 blue shirts, 100 green shirts and 50 orange shirts. Determine the missing probabilities for the following probability distribution. (1pt)

Select one:

a. 1=.40, 2=.30, 3=.20, 4=.10

b. 1=.20, 2=.15, 3=.10, 4=.05

c. 1=2.50, 2=3.33, 3=4.0, 4=5.0

d. 1=.25, 2=.25, 3=.25, 4=.25

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Compute the mean of the following probability distribution for the number of customers per hour:

Enter your answer to one decimal place. (1 pt)

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Fill in the final probability value and compute the mean of the following discrete probability distribution for the scores on a state job qualifying exam. (2pts):

What is the mean score on the exam?

Select one:

a. 12.3

b. 12.9

c. 33.8

d. 73.0

e. 75.0

f. 77.0

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Dave gave a six question quiz to his Statistics students. The students were talented, and no one scored below a 4. Half the students scored 4, 40% scored 5, and 10% scored 6. Compute the mean of this distribution, answer to one decimal place. (1 pt)

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Dave gave a six question quiz to his Statistics students. The students were talented, and no one scored below a 4. Half the students scored 4, 40% scored 5, and 10% scored 6. Compute the variance of this distribution (round answer to one decimal place). (1 pt)

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Dave gave a six question quiz to his Statistics students. The students were talented, and no one scored below a 4. Half the students scored 4, 40% scored 5, and 10% scored 6. Compute the standard deviation of this distribution (round answer to one decimal place). (1 pt)

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Jane has purchased a raffle ticket from her local church for $2.00. (For simplicity assume Jane's ticket is good for any and all prixes.) The following prizes will be awarded:
         Grand Prize:   $1,000
         Second Prize: $250
         Third Prize:     $50

Yesterday was the last day of ticket sales and the church financial director reported that there were 1,000 tickets sold.

What is Jane's expected value for entering this raffle? (2pts)

Select one:

a. $-.70

b. $-.30

c. $.10

d. $.70

e. -$8.70

f. $1,300

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A game is fair if the money you pay to play it equals your expected value from playing it. Consider a game where if you draw a diamond from a standard card deck (4 suits, 52 cards) you win $10. If you get a heart, spade, or club you get nothing. What is the fair value of this game in dollars and cents?

Do not include the "$" sign in your answer. Answer to two decimals. (2pts)

Answer:

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An insurance company sells policies for charity BINGO games. The insurer charges $7,000 per event. If anyone gets BINGO in 5 calls (or less), they win $100,000. If on average the insurance company pays off one winner per every 25 charity events, compute the expected value to the insurer for a single event. (Assume all other costs to the insurer are zero.) (2pts)

Select one:

a. $0

b. $500

c. $1,500

d. $2,000

e. $2,500

f. $3,000

g. $3,500

h. $4,000

i. $4,500

j. $5,000

k. Cannot be determined with the information given.

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A church runs an annual $100,000 one-game BINGO contest. If anyone gets BINGO in 5 calls (or less), they win $100,000. The church buys an insurance policy to cover the possibility of a winner (or winners). Assume the church pays $7,000 for the insurance, and expects to sell 500 BINGO cards at $20 each. It cost the church $300 in advertising for the event, and $200 for other prizes. What is the church's expected value from the event? (2 pts)

Select one:

a. $0

b. $500

c. $1,000

d. $1,500

e. $2,000

f. $2,500

g. $3,000

h. $3,500

i. $4,000

j. $4,500

k. $5,000

l. Cannot be determined with the information givem

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A salesperson makes 12 calls per day, with a 30% chance of a sale on any given call. What are the odds of making exactly 3 successful sales calls today?

Provide your answer to three decimal places.

(Hint: This problem is easiest done using the Binomial Table.) 1 pt.

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A salesperson makes 12 calls per day, with a 30% chance of a sale on any given call. What are the odds of making less than 3 successful sales calls today?

Provide your answer to three decimal places.

(Hint: This problem is easiest done using the Binomial Table.) 1 pt.

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There is a 50% chance that any child born today will have birth trait X. What are the odds that exactly two of the next nine children born at a local hospital will have birth trait x?

Easiest done using the binomial table. Choice answers may be rounded.

(1 pt.)

Select one:

a. 7%

b. 9%

c. 25%

d. 30.2%

e. 45%

X Red Shirts Blue Shirts Green Shirts Orange Shirts P(X) _1_ _2_ _3_ _4_

Explanation / Answer

Question 1: Option (C)

Question 2: Opation (a) Since 200/500=0.4 150/500 = 0.3 100/500 = 0.2 50/100 = 0.10

Question 3: Mean = 0*0.10 + 5*0.30 + 10*0.40 + 15*0.20 = 8.5

Question 4: Missing Probability 1 - 0.75 = 0.25   

Mean = 0.10*50 + 60*0.20 + 70*0.30 + 80*0.25 + 90*0.10 + 100*0.05 = 72

Question 5:

Score : 4 5 6

P(X=x) 0.50 0.40 0.10

Mean = 4*0.5 + 5*0.4 + 6*0.10 = 4.6

Question 6:

E(X2) =42*0.5 + 52*0.4 + 62*0.10 = 21.6

variance = 21.6 - 4.62 = 0.44

Question 7: SD = sqrt(0.44) = 0.6633

Question 8: E(x) = 1000 * 0.001 + 250*0.001 + 50*0.001 = 1.3*100 = 1300

Question 9: E(X) = 20*(13/52) + 0(39/52) = 5

Question 10: E(X) = 100,00*5 /25 =2000

Qiuestion 11:

Question 12: 0.240 = 0.24%

Question 13; 0.795 = 0.80%

Question 14: 0.070 = 7%

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