WK 3 Test

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Jun 12, 2024

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Week 3 Test Your work has been saved and submitted Written May 22, 2024 1:45 PM - May 22, 2024 3:12 PMAttempt 1 of 2 Attempt Score 18 /20-90% Overall Grade (Highest Attempt) 18 / 20-90 % Question 1 1 /1 point It is known that 20% of adult workers have a high school diploma. If a random sample of 10 adult workers is selected, what is the probability that 5 or more of them have a high school diploma? (That is, find P(X = 5) (round to 4 decimal places) Answer: ___0.0328 __ v W Hide question 1 feedback Px >5) =1-P(x <4), in Excel

=1-BINOM.DIST(4,10,0.2,TRUE) Question 2 1 /1 point If random variable X has a binomial distribution with n =7 and P(success) = p =0.6, find the probability that X is at least 6. (That is, find P(X = 6) (round to 4 decimal places) Answer: ___0.1586___ v W Hide question 2 feedback Px >6)=1-P(x <5), in Excel =1-BINOM.DIST(5,7,0.6,TRUE) Question 3 1 /1 point Approximately 8% of all people have blue eyes. A random sample of 20 people is selected, find M. Round to one decimal place. Answer: 1.6 v W Hide question 3 feedback 20%.08 Question 4 1 /1 point Suppose a random variable, x, arises from a binomial experiment. If n = 25, and p = 0.85, find the variance. Round answer to 4 decimal places. Answer: 3.1875 v

W Hide question 4 feedback 25%.85*%.15 Question 5 1 /1 point A coin is flipped 30 times. What is the probability of getting 15 or more heads? Round answer to 4 decimal places. Answer: ___.5722 __ W Hide question 5 feedback Px > 15) =1 -P(x < 14) in Excel =1-BINOM.DIST(14,30,0.5,TRUE) Question 6 0/ 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 1s randomly selected. NAME Single || Double || Triple || Home Run || TOTAL HITS Babe Ruth 1,517 ||506 136 714 2,873 Jackie Robinson [|1,054 (273 54 137 1,518 Ty Cobb 3,603 ({174 295 114 4,189 Hank Aaron 2,294 11624 98 755 3,771 TOTALS 8,468 ||1,577 ||583 1,720 12,351 Find P(hit was made by Ty Cobb|The hit was a Home Run).

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) 0.033 = () 0.066 x (114 ) 0.009 W Hide question 6 feedback 114/1720 Question 7 1 /1 point Find the probability of rolling a sum of two dice that is more than 7. Round answer to 4 decimal places. Answer: 0.4167 v W Hide question 7 feedback Dice outcomes 1 |2 3 4 5 6 ] (1, |a, a, ja, ja, ||, 1) |20 3 |4 |[5) ||6) , 2, |2, |2, |2, |2, |, 1) |20 |3) |4 |[5) ||6) 3 3, |3, B, |3, |3, |G, 1) |20 3) |4 |[5) ||6) 4 4, (4, |4, |4, |4, ||4, 1) |20 |3) |4 |[5) ||6)

: (5, |[(5, ||(5, |[(5, |[(5, (5, 1 12 |13) (|4 |5 ||6) 6 6, |[(6, |6, |[(6, (6, (6, 1 12 |13) (4 |5 ||6) 36 rolls total, 15 up them sum to greater than 7. Which is 8 or more. Probability 15/36 Question 8 1 /1 point A raffle sells 1000 tickets for $35 each to win a new car. What is the probability of winning the car? Round to three decimal places. Answer: W Hide question 8 feedback Only 1 person will win the car Probability = 1/1000 Question 9 1 /1 point An experiment is to flip a fair coin three times. What is the probability of getting exactly two heads? Round to 3 decimal places. Answer: W Hide question 9 feedback TTT TTH THT HTT HHH HHT HTH THH Exactly 2 Heads happens 3 times. Probability = 3/8 0375 _ v

Question 10 1 /1 point A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution. Let X = the number of years a new hire will stay with the company. Let P(x) = the probability that a new hire will stay with the company x years. Complete Table using the data provided. Round to two decimal places. X A X) ‘O 0.12 1 0.18 2 0.30 3 0.15 4 —— 5 0.10 6 0.05 __-0.10___ v W Hide question 10 feedback

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1-(12 + .18 +.30 + .15+ .10 + .05) 1 -.90 Question 11 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| 1 2 3 Probability, P(X=x) [48%|28%|24% What is the probability that a randomly selected part-time student at this college takes at more than 2 courses? (That 1s, find P(X > 2) Answer: ___0.24___ « (round to 2 decimal places) W Hide question 11 feedback Greater than 2 is P(x = 3) = .24 Question 12 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| 1 2 3

Probability, P(X=x) [52%]28%|20% 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 2) ___0.48 __ v (round to 2 decimal places) W Hide question 12 feedback Greater than or equal to 2 is 2 AND 3. P(x =2) + P(x = 3) 28 + .20 Question 13 1 / 1 point Does the following table represent a valid discrete probability distribution? X 1 2 | 3 4 1 5 P(X=x)]0.11]0.06]0.18]0.06]0.96 L Yes ,/O no W Hide question 13 feedback No, since the probabilities do not add up to 1

Question 14 1 /1 point If random variable X has a Poisson distribution with mean = 10, find the probability that X is at least 2. (That is, find P(X = 2) (round to 4 decimal places) 0.9995 v W Hide question 14 feedback Px>2)=1-P(x<1), in Excel =1-POISSON.DIST(1,10,TRUE) Question 15 1 / 1 point If random variable X has a Poisson distribution with mean = 6, find the probability that X is 12. (That is, find P(X=12) (Round answer to 4 decimal places) Answer: 0.0113 v W Hide question 15 feedback In Excel, =POISSON.DIST(12,6,FALSE) Question 16 1 / 1 point Suppose a random variable, x, follows a Poisson distribution. Let u = 2.5 every minute, find the P(X = 125) over an hour. Round answer to 4 decimal places. Answer: 0.9835 v W Hide question 16 feedback New mean per hour = 2.5*60 = 150. P(x = 125) =1 - P(x < 124), in Excel

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=1-POISSON.DIST(124,150,TRUE) Question 17 1 /1 point The mean number of visitors at a national park in one weekend is 55. Assume the variable follows a Poisson distribution. Find the probability that there will be at most 49 visitors at this park in one weekend. (That is, find P(X<49)) (round to 4 decimal places) Answer: ___0.2322_ __ v W Hide question 17 feedback In Excel, =POISSON.DIST(49,55,TRUE) Question 18 1 /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 exactly 4 calls in two hours? Round answer to 4 decimal places. Answer: 0.0051 v W Hide question 18 feedback New mean 2.83/8 = .35375 per hour. 2 *.35375 = .7075 for 2 hours. P(x = 4), in Excel, =POISSON.DIST(4,0.7075,FALSE)

Question 19 0/ 1 point A gumball machine contains 350 grape flavored balls, 400 cherry flavored balls, and 550 lemon flavored balls. What is the probability of getting 1 grape ball, 1 cherry ball, and 1 lemon ball if each ball was removed and then replaced before choosing the next from the machine? % () 0.0347 ) 0.0531 ) 0.0482 = () 0.0350 W Hide question 19 feedback (350/1300)*(400/1300)*(550/1300) Question 20 1 / 1 point The table below shows the preferences for elective courses of students who are undecided about their majors. Philosophy || Digital Art | Film Studies Male 9 16 22 Female 6 18 14

What is the probability of randomly selecting a student who is female or prefers Digital Art? v ) 63.5% ”> 84.7% ) 46.2% ) 21.2% W Hide question 20 feedback P(F or DA) = P(F) + P(DA) - P(F and DA) (38/85)+(34/85) - (18/85) Done

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WK 3 Test

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