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MATH 302 WEEK 3 TEST-with 100%
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A coin is flipped 30 times. Find σ². Round to 1 decimal place. Answer:
Hide Feedback 30.5. Question 2 1 / 1 point Approximately 10% of all people are left-handed. If 200 people are randomly selected, what is the expected number of left-handed people? Round to the whole number. Do not use decimals. Answer: 20 Hide Feedback 200*. Question 3 1 / 1 point Suppose a random variable, x, arises from a binomial experiment. If n = 14, and p = 0.13, find the P(X ≤ 3) using Excel. Round answer to 4 decimal places. Answer:
Hide Feedback In Excel, =BINOM.DIST(3,14,0.13,TRUE) Question 4 1 / 1 point It is known that 50% of adult workers have a high school diploma. If a random sample of 5 adult workers is selected, what is the probability that more than 3 of them have a high school diploma? (That is, what is P(X>3) (round to 4 decimal places) Answer:
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P(x > 3) = 1 - P(x ≤ 3), in Excel =1-BINOM.DIST(3,5,0.5,TRUE) Question 5 1 / 1 point Suppose a random variable, x, arises from a binomial experiment. If n = 25, and p = 0.85, find the P(X = 15) using Excel. Round answer to 4 decimal places. Answer:
Hide Feedback In Excel, =BINOM.DIST(15,25,0.85,FALSE) Question 6 1 / 1 point The table of data obtained from WWW.BASEBALL-ALMANAC.COM shows hit information for four well known baseball players. Suppose that one hit from the table is randomly selected. NAME Single Double Triple Home Run TOTAL HITS Babe Ruth 1,517 506 136 714 2, Jackie Robinson 1,054 273 54 137 1, Ty Cobb 3,603 174 295 114 4, Hank Aaron 2,294 624 98 755 3, TOTALS 8,468 1,577 583 1,720 12, Find P (hit was a Home Run|The hit was made by Ty Cobb ). Question options:
Order Matters =PERMUT(20,9) Order Matters =PERMUT(20,9) Question 8 1 / 1 point Find the probability of rolling a sum of two dice that is a 7 or a 12. Round answer to 4 decimal places. Answer:
Hide Feedback Dice outcomes 1 2 3 4 5 6 1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) 2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) 3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) 4 (4,^ 1)^ (4,^ 2)^ (4,^ 3)^ (4,^ 4)^ (4,^ 5)^ (4,^ 6) 5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) 6 (6,^ 1)^ (6,^ 2)^ (6,^ 3)^ (6,^ 4)^ (6,^ 5)^ (6,^ 6) Only 7 ways to sum to exactly 7 or exactly 12 7/ Question 9 1 / 1 point The number of M&M's for each color found in a case were recorded in the table below. Blue = 481, Brown = 371, Green = 483, Orange = 544, Red = 372, Yellow = 369 Total = 2620 What is the probability of selecting a red M&M? Round answer to 4 decimal places. Answer:
Hide Feedback 372/ Question 10 1 / 1 point Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. Number of Courses ,
x
Probability, P ( X = x ) 46%^ 28%^ 26%
What is the probability that a randomly selected part-time student at this college takes at least 2
courses? (That is, find P(X ≥ 2)
Answer:
(round to 2 decimal places) Hide Feedback .28 +. Question 11 1 / 1 point The random variable X = the number of vehicles owned. Find the probability that a person owns less than 2 vehicles. Round to two decimal places. x 0 1 2 3 4
P(X = x ) 0.1^ 0.35^ 0.25^ 0.2^ 0.
add up to 1 Question 13 1 / 1 point Let X be the number of courses taken by a part-time student at a college. The following table shows the probability distribution of X with probability as a percentage. Number of Courses ,
x
Probability, P ( X = x ) 55%^ 28%^ 17%
What is the probability that a randomly selected part-time student at this college takes at least 2 courses? (That is, find P(X ≥ 2 ) Answer:
(round to 2 decimal places) Hide Feedback .28 +. 17 Question 14 0 / 1 point There are on average 5 old growth Sitka Spruce trees per 1/8 of an acre in a local forest. Find the probability that that there are exactly 30 Sitka Spruce trees in 1 acre in a remote part of the forest that is scheduled to be logged next year. Round answer to 4 decimal places. Answer: . Hide Feedback New mean per 1 acre = 5*8= 40. P(x = 30), in Excel =POISSON.DIST(30,40,FALSE)
Question 15 0 / 1 point A bank gets an average of 11 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 9 or more customers at this bank in one hour. (That is, find P(X ≥ 9)) (round to 4 decimal places) Answer:
Hide Feedback P(X≥9) = 1 - P(x ≤ 8), in Excel =1-POISSON.DIST(8,11,TRUE) Question 16 0 / 1 point The number of rescue calls received by a rescue squad in a city follows a Poisson distribution with an average of 2.83 rescues every eight hours. What is the probability that the squad will have at most 2 calls in an hour? Round answer to 4 decimal places. Answer: . Hide Feedback New mean = 2.83/8 = .35375 per hour. P(x ≤ 2), in Excel =POISSON.DIST(2,0.35375,TRUE) Question 17 0 / 1 point The mean number of visitors at a national park in one weekend is 52. Assume the variable follows a Poisson distribution. Find the probability that there will be 58 visitors at this park in one weekend. (That is, find P(X=58) (Round answer to 4 decimal places) Answer: . Hide Feedback In Excel, =POISSON.DIST(58,52,FALSE)
Question 20 0 / 1 point You see a game at a local fair. You have to throw a dart at a color wheel. Each section on the color wheel is equal in area. Let B = the event of landing on blue. Let R = the event of landing on red. Let G = the event of landing on green. Let Y = the event of landing on yellow. If you land on Y, you get the grand prize. Find P(Y). Question options:
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1 Yellow piece, 1/ 1 Yellow piece, 1/ Question 1 1 / 1 point Approximately 8% of all people have blue eyes. Out of a random sample of 20 people, what is the probability that at most 2 of them have blue eyes? Round answer to 4 decimal places. Answer:
Hide Feedback P(x ≤ 2), in Excel =BINOM.DIST(2,20,0.08,TRUE) Question 2 1 / 1 point It is known that 40% of adult workers have a high school diploma. If a random sample of 10 adult workers is selected, what is the expected number of adult workers with a high school diploma? (That is, what is E(X)?) Round to the whole number. Do not use decimals. Answer: 4 Hide Feedback 10*. Question 3 1 / 1 point If random variable X has a binomial distribution with n=15 and P(success) =p= 0.6, find the mean of X. That is, find E(X). Round to the whole number. Do not use decimals. Answer: 9 Hide Feedback
NAME Single Double Triple Home Run TOTAL HITS Jackie Robinson 1,054 273 54 137 1, Ty Cobb 3,603 174 295 114 4, Hank Aaron 2,294 624 98 755 3, TOTALS 8,468 1,577 583 1,720 12, Find P (hit was made by Hank Arron|The hit was a Single). Question options:
Hide Feedback 2294/ Question 7 1 / 1 point The California license plate has one number followed by three letters followed by three numbers. How many different license plates are possible? Do not use commas in your answer. Answer: 175760000 Hide Feedback
Question 8 1 / 1 point In a box there are 3 red cards and 5 blue cards. The cards are well-shuffled. If you pick a card without looking at the box, what is the probability that you pick a red card? (round to 3 decimal places) Answer:
Hide Feedback 3/ Question 9 1 / 1 point In the game of roulette, there is a wheel with spaces marked 0 through 36 and a space marked 00. Find the probability of winning if you pick the number 30 and it comes up on the wheel. Round your answer to 3 decimal places. Answer:
Hide Feedback There is only 1 way to land on 30 and there are 38 total possibilities. 1/ Question 10 0 / 1 point The random variable X = the number of vehicles owned. Find the expected number of vehicles owned. Round answer to two decimal places. Number of Courses ,
x
Probability, P ( X = x ) 0.2^ 0.35^ 0.25^ 0.1^ 0.
Answer:
yes no Hide Feedback No, since the probabilities do not add up to 1 Question 13 1 / 1 point Does the following table represent a valid discrete probability distribution?
x^1 2 3 4
P ( X =
x )
Question options: Yes No Hide Feedback No, since the probabilities do not add up to 1
Question 14 1 / 1 point Computer Help Hot Line receives, on average, 14 calls per hour asking for assistance. What is the probability that the company will receive 3 calls in a 12 minute period? Round answer to 4 decimal places. Answer:
Hide Feedback New Mean = 14/60 = .23333 per hour. For 12 hours 12*.233333. P(x = 3), in Excel =POISSON.DIST(3,2.8,FALSE) Question 15
point A coffee shop serves an average of 75 customers per hour during the morning rush. Find the probability that 80 customers arrive in an hour during tomorrow's morning rush. Round answer to 4 decimal places. Answer:
Hide Feedback P(x = 80), in Excel =POISSON.DIST(80,75,FALSE) Question 16 1 / 1 point The mean number of visitors at a national park in one weekend is 47. Assume the variable follows a Poisson distribution. Find the probability that there will be at most 55 visitors at this park in one weekend. (That is, find P(X ≤ 55)) (round to 4 decimal places) Answer:
Hide Feedback In Excel, =POISSON.DIST(55,47,TRUE)
Hide Feedback 6 chances to win out of 38 possibilities. Question 20 1 / 1 point A box is filled with several party favors. It contains 12 hats, 15 noisemakers, 10 finger traps, and 5 bags of confetti. Let H = the event of getting a hat. Let N = the event of getting a noisemaker. Let F = the event of getting a finger trap. Let C = the event of getting a bag of confetti. Find P(N). Question options:
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Question 1 0 / 1 point It is known that 50% of adult workers have a high school diploma. If a random sample of 6 adult workers is selected, what is the probability that 3 or more of them have a high school diploma? (That is, find P(X ≤ 3) (round to 4 decimal places) Answer:
- (round to 4 decimal places) Answer:
Hide Feedback P(X ≥ 3) = 1 - P(x ≤ 2), in Excel =1-BINOM.DIST(2,6,0.5,TRUE) Question 2 1 / 1 point Approximately 8% of all people have blue eyes. Out of a random sample of 20 people, what is the probability that 2 of them have blue eyes? Round answer to 4 decimal places. Answer:
Hide Feedback P(x = 2), in Excel, =BINOM.DIST(2,20,0.08,FALSE) Question 3 1 / 1 point If random variable X has a binomial distribution with n =10 and P(success) =p =0.2, find the probability that X is less than 6. (That is, find P(X<6) Answer: (round to 4 decimal places)
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