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Jeopardy Final Jeopardy Prob. Dist. Linear Comb Density Curves Binom Geom/ Expect Norm Q $100 Q $200 Q $300 Q $400 Q $500

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$100 Question from Prob. Dist What is the probability when x=3? x01234 P(x)0.280.140.13 0.24

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$100 Answer from Prob Dist 1 - (.28+.14+.13+.24) 1 -.79.21

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$200 Question from Prob Dist What is the P(x > 2)? x012345 P(x)0.040.060.220.280.240.16

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$200 Answer from Prob Dist P(x > 2) = P(3) + P(4) +P(5) =.28 +.24 +.16 = 0.68

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$300 Question from Prob Dist Find the mean & standard deviation x012345 P(x)0.040.060.220.280.240.16

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$300 Answer from Prob Dist

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$400 Question from Prob Dist Find the probability that x is within 2 deviations of the mean. x012345 P(x)0.030.070.230.330.240.1

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$400 Answer from Prob Dist Mean = 2.98 St. Dev. = 1.19 Mean ±2Dev 2.98 ± 2(1.19) 0.6 to 5.36 Answer: 0.97

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$500 Question from Prob Dist The distribution above represents the number of broken eggs in a carton. What is the probability that I randomly choose two cartons and exactly the both have exactly ten unbroken eggs? x012345 P(x)0.330.270.180.120.060.04

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$500 Answer from Prob Dist Ten unbroken = 2 broken P(X=2 and x=2) = 0.18 * 0.18 = 0.0324

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$100 Question from Linear Comb Find: MeanSt. Dev A143 B224

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$100 Answer from Linear Comb 3(14)+4(22)+5 = 135

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$200 Question from Lin Comb Find: MeanSt. Dev A143 B224

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$200 Answer from H2 Answer:

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$300 Question from Lin Comb The following are the mean times and standard deviations for the runners on a relay race team. Find the mean time for the race and the standard deviation. MeanSt. Dev Ed1.10.2 Mary1.50.3 Ted1.40.1 Julie1.30.15

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$300 Answer from Lin Comb Answer:

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$400 Question from Lin Comb x = #hours246810 P(x)0.140.180.220.250.21 The following represents the number of hours of work per doll and number of dolls that Mary makes. She gets paid $4 per hour and $20 per doll and there is a flat cost of $50 for supplies. Find the average amount of money that Mary makes and the standard deviation. y = #dolls47101215 P(y)0.120.140.280.320.14

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$400 Answer from Lin Comb Mean: 4(6.42)+20(10.2) – 50 = $179.68 St. Dev:

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$500 Question from Lin Comb The mean annual salary of employees at a company is $36,000 with a variance of $15,202,201. At the end of the year, each employee receives a $2000 bonus and a 4% raise (based on salary). What is the mean and standard deviation of the new salaries?

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$500 Answer from H2 Mean: St. Dev:

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$100 Question from Density Find P(x < 6) 218

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$100 Answer from Density A=bh 1=16h 0.0625=h A = 0.0625 * 4 A = 0.25

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$200 Question from Density Find the height. 16

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$200 Answer from H3 A=1/2 bh 1=1/2 ( 16)h 1=8h 0.125 = h

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$300 Question from Density Find P(X < 6) 20

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$300 Answer from Density 1=.5(20)H 1=10H 0.1 = H

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$400 Question from Density Find P(x < 7) 40

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$400 Answer from Density

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$500 Question from Density Find P(x < 18) 20

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$500 Answer from Density

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$100 Question from Binomial In a recent survey they found that 25% of U.S. adults prefer texting because “it’s great for flirting.” In a sample of 50, what is the mean & standard deviation of the number who prefer texting due to the ease of flirting

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$100 Answer from Binomial Mean: St. Dev:

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$200 Question from Binomial A survey found that 41% of women in the U.S. consider reading their favorite leisure-time activity. If I randomly select 12 women, find the probability that exactly 7 consider reading their favorite leisure-time activity. (Use formula)

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$200 Answer from Binomial

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$300 Question from Binomial A survey found that 72% of people in the U.S. prefer having a dog as a pet than a cat. What is the probability that in a sample of 82 people, less than 57 prefer a dog? (Use calculator)

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$300 Answer from Binomial P(x < 57) = binomcdf (82, 0.72, 56) = 0.2626

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$400 Question from Binom A survey found that 72% of people in the U.S. prefer having a dog as a pet than a cat. What is the probability that in a sample of 59 people at least 40 prefer a dog? (Use calculator)

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$400 Answer from Binom P(x 40) = 1 – binomcdf (59, 0.72, 39) = 1 – 0.1923 = 0.8077

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$500 Question from Binom Suppose we have a random variable X where the probability associated with the value k is For k = 0, 1, 2,….12. What is the mean of X?

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$500 Answer from Binomial Mean = 12 (0.22) = 2.64

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$100 Question from Geometric The probability that a student passes the written test for a private pilot’s license is 0.68. what is the probability that a student will not pass until the third attempt?

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$100 Answer from Geometric P(x=3) = 0.32 2 *0.68 = 0.0696

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$200 Question from Geometric 29% of American teens say that they would break up with their boyfriend/girlfriend for $10,000. What is the probability that while interviewing teens, you find one that agrees within the first three asked?

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$200 Answer from Geometric P(x 3) =.29 + (.71*.29) + (.71 2 *.29) =.29 +.2059 + 0.1462 = 0.6421

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$300 Question from Geometric A glass manufacturer finds that 1 in every 500 glass items produced is warped. Find the probability that the first warped glass item is in the first four checked.

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$300 Answer from Geometric P(x 4) =.002 + (.998*.002)+(.998 2 *.002) + (.998 3 *.002) =.002 +.001996 +.001992 +.00199 = 0.00798

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$400 Question from Geometric A basketball player has a 74% chance of making a free throw. Find the probability that the first free throw shot he makes is on the third or fourth attempt.

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$400 Answer from Geometric P(x=3 or x=4) = (.26 2 *.74) + (.26 3 *.74) = 0.0500 + 0.0130 = 0.0630

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$500 Question from Geometric Two dice are rolled. If you roll a sum of 12 you can win $100. You can win $50 for a sum of 10 or $5 for a sum of 8. If it costs $10 to play this game, find the expectation of the game.

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$500 Answer from H5

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$100 Question from Normal The mean annual consumption of peanuts are normally distributed with a mean of 5.9 pounds per person and a standard deviation of 1.8 pounds per person. What percent of people annually consume less than 4.5 pounds of peanuts per person?

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$100 Answer from Normal

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$200 Question from Normal The thicknesses of washers produced by a machine are normally distributed, with a mean of 0.425 inch and a standard deviation of 0.005 inch. A washer is selected at random, find the probability that the washer is between 0.423 and 0.426 inch thick?

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$200 Answer from Normal

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$300 Question from Normal The braking distances of a sample of Nissan Altimas are normally distributed with a mean of 129 feet and a standard deviation of 5.18 ft. What is the longest braking distance one of these Nissan Altimas could have and still be in the bottom 5%?

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$300 Answer from Normal

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$400 Question from H6 The average time spent sleeping (in hours) for medical residents is normally distributed with a mean of 6.1 hours and a standard deviation of 1.02 hours. Between what two values does the middle 40% of the sleep times lie?

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$400 Answer from Normal

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$500 Question from Normal The mean of a standardized test is 100. If the 85 th percentile score is 110, find the standard deviation of the test.

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$500 Answer from Normal

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Final Jeopardy What are the major differences between binomial and normal distributions?

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Final Jeopardy Answer Binomial – discrete with fixed number of trials with two possibilities Normal – continuous data

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Chapter 7 Random Variables and Discrete Distributions.

Chapter 7 Random Variables and Discrete Distributions.

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