Probability and Linear Combination Questions and Answers
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Jeopardy Final Jeopardy
$100 Question from Prob. Dist What is the probability when x=3?
$100 Answer from Prob Dist 1 - (.28+.14+.13+.24) 1 - .79 .21
$200 Question from Prob Dist What is the P(x > 2)?
$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
$400 Question from Prob Dist Find the probability that x is within 2 deviations of the mean.
$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?
$500 Answer from Prob Dist Ten unbroken = 2 broken P(X=2 and x=2) = 0.18 * 0.18 = 0.0324
$100 Answer from Linear Comb 3(14)+4(22)+5 = 135
$200 Answer from H2 Answer:
$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.
$300 Answer from Lin Comb Answer:
$400 Question from Lin Comb 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.
$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 2 18 Find P(x < 6)
$100 Answer from Density A=bh 1=16h 0.0625=h A = 0.0625 * 4 A = 0.25
$200 Question from Density 16 Find the height.
$200 Answer from H3 A=1/2 bh 1=1/2 ( 16)h 1=8h 0.125 = h
$300 Question from Density 20 Find P(X < 6)
$300 Answer from Density 1=.5(20)H 1=10H 0.1 = H
$400 Question from Density 40 Find P(x < 7)
$500 Question from Density 20 Find P(x < 18)
$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) = 0.322 *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) + (.712*.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)+(.9982 *.002) + (.9983*.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) = (.262*.74) + (.263*.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.
