8,4-8.5 Practice Questions Part 1

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A raffle ticket costs $5. First and second prize winners will be drawn at random. Theprobability of winning the $100 first prize is 1/40 and the probability of winning the525 second prize is 1/20. What is the mean winnings for one play, taking into accountthe $5 cost of the ticket?

Suppose a game has three outcomes, A, B, and C with probabilities P(A) = 0.2, P(B) --0.3, and P(C) = 0.5. A player will receive $3 when outcome A occurs, $4 whenoutcome B occurs, and will have to pay $2 when outcome C occurs. What is the meanvalue of one trial of the game? ÿ -- I

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3. At a certain discount store, the number of people in checkout lines varies. Theprobability model for the number of people in a randomly chosen line is:Number in 0 1 2 3 4 5lineProbability 0.08 0.15 0.20 0.22 0.15 0.20What is the mean number of people in a line?

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4. A fair die is rolled. Ifa number 1or 2 appears, you will receive $5. If any othernumber appears, you will pay $2. What is the mean value of one trial of this game?

i5. The marketing department of an electronics manufacturer has done research on the

number of television sets owned by families in a large town. The probability model forthe number of sets owned by a randomly chosen family is given below. What is themean number of sets per family?Number ofsets

Probability

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0.04 0.34 0.47 0.15

+.7o ,s) !. The shelf life of a battery produced by one major company is known to be normally

distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. Whatis the upper quartile of battery shelf life?

8.4-8.5 Practice Questions Part 1

. The length of students' college careers at Anytown University is known to be normallydistributed, with a mean length of 5.5 years and a standard deviation of 1.75 years.What is the lower quartile for the length of students' careers at Anytown University?

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8. The scores of students on a standardized test form a normal distribution with a meanof 300 and a standard deviation of 40.for this test? -%

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What are the lower and upper quartile scores

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&ÿ3, a.9. The mean length of time, per week, that students at a certain school spend on their

homework is 24.3 hours, with a standard deviation of 1.4 hours. Assuming thedistribution of study times is normal, what percent of students spend more than25.238 hours per week on homework?

10. The scores of students on a standardized test are normally distributed with a mean of300 and a standard deviation of 40. What is the probability that a randomly chosenstudent scores below 273.2 on the test?

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11. The annual income of residents in a county is $42,000 with a standard deviation of$10,000. Between what two values do 95% of the incomes of county residents lie?

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12. The shelf life of a battery produced by one major company is known to be normallydistributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. Whatrange of years contains 68% of all battery shelf lives?

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13. The scores of students on a standardized test are normally distributed with a mean of300 and a standard deviation of 40. Between what two values do 99.7% of the test

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8.4-8.5 Practice Questions Part I

Part 224. The mean length of time, per week, that students at a certain school spend on their

homework is 24.3 hours, with a standard deviation of 1.4 hours. Assuming thedistribution of study times is normal, what percent of students study between 22.9and 25.7 hours? ,_.

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I,H _,:1.5. The length of students' college careers at Anytown University is known to be normally

distributed, with a mean length of 5.5 years and a standard deviation of :1..75 years.What percent of students have college careers lasting between 2 and 9 years?

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:1.6. The shelf life of a battery produced by one major company is known to be normallydistributed, with a mean life of 3.5 years and a standard deviation of 0.75 gears. Whatpercent of batteries last between 1.25 and 5.75 years?

17. The annual income of residents in a certain county is normally distributed, with amean of $42,000 and a standard deviation of $10,000. What is theprobability__that arandomly chosen resident has income over S52,000?

18. The weight of potato chip bags filled by a machine at a packaging plant is normmlydistributed, with a mean of 15.0 ounces and a standard deviation of 0.2 ounces. Whatis the probability that a randomly chosen bag will weigh less than 14.6 ounces?

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The weight of potato chip bags filled by a machine at a packaging plant is normallydistributed, with a mean of 15.0 ounces and a standard deviation of 0.2 ounces. Whatis the probability that a randomly chosen bag will weigh more than 15.6 ounces?

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8.4-8.5 Practice Questions Part i

20. Below is a probability model for the number of automobiles owned by a randomlychosen family in a large town.Number of automobiles 0Probability 0.15

What is the mean number of automobiles owned?1 2 3

0.20 0.55 0.10

21. Suppose a game has four outcomes, A, B, C, and D. The probability of outcome A is0.4, the probabilities of each of the other outcomes is 0.2. A player receives $2 ifoutcome A occurs, $3 if outcome B occurs, $1 if outcome C occurs, and must pay $5 ifoutcome D occurs. What is the mean value of one trial of this game?

22. The mean value of one trial of a carnival game is -$.05. Explain what this means.

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Suppose a trial consists of rolling a single die and reporting the number that is rolled.What are the possible outcomes? Are they equally likely?

Suppose a trial consists of rolling two dice and reporting the sum of the numbersrolled. What are the possible outcomes? Are they equally likely?

25. Suppose a trial consists of rolling two dice and and reporting the smaller of the twonumbers rolled? What are the possible outcomes? Are they equally likely?

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The mean weight of a collection of potatoes in a shipment to a fruit market is 1.3 Ibs,with a standard deviation of 0.35 Ibs. The distribution of weights is approximatelynormal. What is the probability that one potato chosen at random will weigh morethan 1.65 Ibs? ÿJÿ/ ÿ:,ÿ ÿ ÿ,'ÿvÿ ÿ>t__ÿ ÿ -ÿ

The mean weight of a collection of potatoes in a shipment to a fruit market is 1.3 Ibs,with a standard deviation of 0.35 Ibs. The distribution of weights is approximatelynormal. What fraction of the potatoes in the shipment will weigh between 0.25 and2.35 Ibs?

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