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

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

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

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

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

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

\$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

\$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

\$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

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

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

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

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

\$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

\$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

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

\$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?

\$500 Answer from H2 Mean: St. Dev:

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

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

\$200 Question from Density Find the height. 16

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

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

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

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

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

\$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

\$100 Answer from Binomial Mean: St. Dev:

\$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)

\$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)

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

\$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)

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

\$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?

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

\$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?

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

\$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?

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

\$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.

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

\$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.

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

\$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.

\$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?

\$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?

\$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%?

\$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?

\$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.

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

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

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