Probability and Statistics Homework: Week 3 Knowledge Check

Week 3 Knowledge Check Homework Practice Questio… Attempt 3 of 4 Written Dec 24, 2023 9:03 PM - Dec 24, 2023 9:23 PM Attempt Score 9 / 20 - 45 % Overall Grade (Highest Attempt) 18 / 20 - 90 % Question 1 1 / 1 point ___ 4___ Hide ques±on 1 feedback Question 2 0 / 1 point ___ .05___ (9) Hide ques±on 2 feedback 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: 10*.4 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: 15*.6

Question 3 0 / 1 point ___ 0.5___ (7.5) Hide ques±on 3 feedback Question 4 0 / 1 point ___ 0.9021___ (1.2583) Hide ques±on 4 feedback Question 5 0 / 1 point ___ 0.7879___ (0.2711, .2711) Hide ques±on 5 feedback Question 6 1 / 1 point The table shows a random sample of musicians and how they learned to play their instruments. A coin is flipped 30 times. Find σ ². Round to 1 decimal place. Answer: 30*.5*.5 Suppose a random variable, x, arises from a binomial experiment. If n = 14, and p = 0.13, find the standard deviation. Round answer to 4 decimal places. Answer:___ In Excel, =SQRT(14*0.13*0.87) 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: P(x = 2), in Excel, =BINOM.DIST(2,20,0.08,FALSE)

Gender Self-Taught Studied in School Private Instruction Total Female 12 38 22 72 Male 19 24 15 58 Total 31 62 37 130 Find P (musician is a female AND had private instruction). Hide ques±on 6 feedback Question 7 1 / 1 point ___ 0.25___ Hide ques±on 7 feedback Question 8 0 / 1 point 0.17 0.12 0.88 0.83 22/130 There are 4 answers for a single question on the exam and only one answer is correct. If a student guesses the answer for this question, what is the probability that the student selects the correct answer? (round to 2 decimal places) Answer: 4 possibilities but only 1 correct answer. 1/4 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

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___ 17576000___ (175760000, 175,760,000, 175760,000, 175,760000) Hide ques±on 8 feedback Question 9 1 / 1 point ___ 8000000___ Hide ques±on 9 feedback Question 10 1 / 1 point ___ 0.45___ Hide ques±on 10 feedback commas in your answer. Answer: 1 * 26 3 * 10 3 How many different phone numbers are possible in the area code 503, if the first number cannot start with a 0 or 1? Do not use commas in your answer. Answer: First number has 8 different choice then the last 6 numbers can be any number. 8 * 10 6 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 0.1 Answer: Less than 2 is P(x = 0) + P(x = 1)

Question 11 0 / 1 point ___ 1.85___ (1.55) Hide ques±on 11 feedback Question 12 1 / 1 point ___ 0.3___ Hide ques±on 12 feedback .1 + .35 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 0 1 2 3 4 Probability, P ( X = x ) 0.2 0.35 0.25 0.1 0.1 Answer: 0*.2 + 1*.35 + 2*.25 + 3*.1 + 4*.1 The random variable X = the number of vehicles owned. Find the P(X > 2). Round to two decimal places. x 0 1 2 3 4 P(X = x ) 0.1 0.35 0.25 0.2 0.1 Answer: Greater than 2, is P(x = 3) + P(x = 4) .2 + .1

Question 13 1 / 1 point ___ 0.54___ Hide ques±on 13 feedback Question 14 0 / 1 point ___ 0.0148___ (0.0521, .0521) Hide ques±on 14 feedback Question 15 0 / 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 ) 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) .28 + .26 A coffee shop serves an average of 72 customers per hour during the morning rush. Find the probability that less than 59 customers arrive in an hour during tomorrow's morning rush. Round answer to 4 decimal places. Answer: P(x < 59) = P(x ≤ 58), In Excel =POISSON.DIST(58,72,TRUE)

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___ 0.7219___ (0.0722, .0722) Hide ques±on 15 feedback Question 16 0 / 1 point ___ 0.8152___ (0.8815, .8815) Hide ques±on 16 feedback Question 17 1 / 1 point ___ 0.8774___ Hide ques±on 17 feedback A bank gets an average of 8 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 11 customers at this bank in one hour. (That is, find P(X=11) (Round answer to 4 decimal places) Answer: In Excel, =POISSON.DIST(11,8,FALSE) A bank gets an average of 15 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 11 or more customers at this bank in one hour. (That is, find P(X ≥ 11) (round to 4 decimal places) Answer: P(X≥11) = 1 - P(x ≤ 10), in Excel =1-POISSON.DIST(10,15,TRUE) There are 6.5 accidents, on average, at an intersection. Assume the variable follows a Poisson distribution. Find the probability that there will be 9 or less accidents at this intersection. (That is, find P(X≤9) (round to 4 decimal places) Answer: In Excel, =POISSON.DIST(9,6.5,TRUE)

Question 18 0 / 1 point ___ 0.4623___ (0.9943, .9943) Hide ques±on 18 feedback Question 19 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). Hide ques±on 19 feedback Question 20 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: ____ New mean = 2.83/8 = .35375 per hour. P(x ≤ 2), in Excel =POISSON.DIST(2,0.35375,TRUE) 0.13 0.12 0.36 0.24 15/42

A drug is reported to benefit 40% of the patients who take it. If 6 patients take the drug, what is the probability that 4 or more patients will benefit? Hide ques±on 20 feedback Done 0.179 0.862 0.667 0.138 P(x 4) = 1 - P(x 3), in Excel =1-BINOM.DIST(3,6,0.4,TRUE)

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