0 Question 1 [3 0/1 pt '0 3 23 99 G) Details Multiple-choice questions each have 6 possible answers, one of which is correct. Assume that you guess the answers to 3 such questions. Use the multiplication rule to find the probability that the first two guesses are wrong and the third is correct. That is, find P(WWC), where C denotes a correct answer and W denotes a wrong answer. (round answer to 4 decimal places) P(WWC') 2 What is the probability of getting exactly one correct answer when 3 guesses are made? (round answer to 4 decimal places) P(exactly one correct answer) = Question Help: Q Written Example Submit Question 0 Question 2 E on pt '0 3 8 99 (9 Details Katy is catering an event this weekend and needs to begin prepping. There are 230 guests scheduled to attend the event. On the menu is a chicken dish, a salmon dish, and a vegetarian dish. Although people often do have a preference for fish and chicken, she is particularly concerned with having enough vegetarian dishes available. Unfortunately, the event did not ask for the guests preference in advance. However, one thing that Katy does know is that for this locality, she has found that the percentage of people who are vegetarian to be around 8%. She knows, though, that just purely making 8% of meals may not be enough, and there is still a high chance of running out of vegetarian meals. She wants to ensure that the probability of running out of vegetarian meals is low. Having taken a Statistics course in college, she vaguely recalls that a Binomial distribution may help her solve this problem, but she needs help. First, verify the conditions for a binomial distribution. Explain how you know each of the conditions are satisfied. Binary - Each trial can result in a success or failure. What would ou consider a success or failure? Identical and Independent Trials - Each trial has the same probability of success, and are independent of each other. What is the probability of success for each trial? Are each trial independent {think 5% rule)? Number of trials are fixed - Do we know the number of trials? A Hint: You can consider each individual person deciding what to eat as a trial. Identify the binomial parameters. Write p and q as a decimal. 0 Question 3 E on pt '0 3 5:5 99 G) Details Using the Binomial distribution, If n=6 and p=0.6, find P(x=4) i J 0 Question 4 E 011 pt '0 3 3 99 (9 Details You are taking a 15 question multiple choice test, where each question has 3 possible answers. Identify n and p. Write p as a fraction. Find the mean and standard deviation of the binomial random variable. Write your answers as a fraction, expression or decimal with at least 4 decimal places. H H i What would be an unusually high number of correct questions? Give your answer in the box above as a whole number. ' ' or more correct. Submit Question Question 5 Go/1 pt 0 3 # 99 0 Details A poll is given, showing 45% are in favor of a new building project. If 10 people are chosen at random, what is the probability that exactly 6 of them favor the new building project? Question Help: Video Submit Question Question 6 60/1 pt 0 3 # 99 0 Details A manufacturing machine has a 9% defect rate. If 8 items are chosen at random, what is the probability that at least one will have a defect? Submit Question Question 7 G 0/1 pt 0 3 99 0 Details Assume that a procedure yields a binomial distribution with a trial repeated n = 7 times. Use either the binomial probability formula (or technology) to find the probability of * = 2 successes given the probability p = 0.52 of success on a single trial. (Report answer accurate to 4 decimal places.) P(X = k) = Submit Question Question 8 60/1 pt 0 3 # 99 0 Details Assume that a procedure yields a binomial distribution with a trial repeated n = 9 times. Use either the binomial probability formula (or technology) to find the probability of * = 6 successes given the probability p = 76 % of success on a single trial. (Report answer accurate to 4 decimal places.) P(X = k) = Submit Question Question 9 Go/1 pt 0 3 # 99 0 Details Assume that a procedure yields a binomial distribution with a trial repeated n = 15 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k = 9 successes given the probability p = 19/30 of success on a single trial. (Report answer accurate to 4 decimal places.) P(X = k) = Submit Question Question 10 60/1 pt 0 3 # 99 0 Details Assume that a procedure yields a binomial distribution with a trial repeated n = 5 times. Use some form of technology to find the probability distribution given the probability p = 0.844 of success on a single trial. (Report answers accurate to 4 decimal places.) k P(X - k) Question Help: Video Submit QuestionQuestion 11 6 0/1 pt 3 # 99 0 Details The television show Lett3rs has been successful for many years. That show recently had a share of 15, which means, that among the TV sets in use, 15% were tuned to Letters. An advertiser wants to verify that 15% share value by conducting its own survey, and a pilot survey begins with 12 households have TV sets in use at the time of a Letters broadcast. Find the probability that none of the households are tuned to Lett3rs. P(none) = Find the probability that at least one household is tuned to Lett3rs. P(at least one) = Find the probability that at most one household is tuned to Lett3rs. P(at most one) = If at most one household is tuned to Letters, does it appear that the 15% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Letters unusual?) No, it does not seem wrong. It is still reasonable to observe at most one household tuned to Lett3rs given a 15% share. Yes, it appears to be wrong. Observing at most one household tuned to Letters would be unusual to see if the show had a share of 15%. Question Help: ) Video Submit Question Question 12 6 0/1 pt 0 3 99 0 Details A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly selects and tests 28 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. What is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 8% rate of defects? (Report answer as a decimal value accurate to four decimal places.) P(accept shipment) - Submit Question Question 13 60/1 pt 0 3 # 99 0 Details The Wilson family was one of the first to come to the U.S. They had 4 children. Assuming that the probability of a child being a girl is .5, find the probability that the Wilson family had: at least 3 girls? at most 2 girls? Submit Question Question 14 G 0/1 pt 0 3 # 99 0 Details A high school baseball player has a 0.186 batting average. In one game, he gets 8 at bats. What is the probability he will get at least 3 hits in the game? Submit Question . Question 15 60/1 pt 0 3 # 99 0 Details If a seed is planted, it has a 85% chance of growing into a healthy plant. If 11 seeds are planted, what is the probability that exactly 1 doesn't grow? Question Help: Video Submit Question Question 16 Go/1 pt 0 3 99 0 Details A small regional carrier accepted 12 reservations for a particular flight with 11 seats. 9 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 44% chance, independently of each other. (Report answers accurate to 4 decimal places.) Find the probability that overbooking occurs. Find the probability that the flight has empty seats Question Help: Written Example Submit QuestionQuestion 17 0/1 pt 0 3 # 99 0 Details After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only three women among the last 18 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women. Help her address the charge of gender discrimination by finding the probability of getting three or fewer women when 18 people are hired, assuming that there is no discrimination based on gender. (Report answer accurate to 8 decimal places). P(at most three) = Because this is a serious claim, we will use a stricter cutoff value for unusual events. We will use 0.5% as the cutoff value (1 in 200 chance of happening by chance). With this in mind, does the resulting probability really support such a charge? no, this does not support a charge of gender discrimination O yes, this supports a charge of gender discrimination Submit Question . Question 18 0/1 pt 0 3 # 99 0 Details About 1% of the population has a particular genetic mutation. 800 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 800. Submit Question Question 19 0/1 pt 0 3 # 99 0 Details About 4% of the population has a particular genetic mutation. 300 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 300. Round your answer to three decimal places Question Help: Read Submit Question Question 20 60/1 pt 0 3 99 0 Details When taking a 7 question multiple choice test, where each question has 5 possible answers, it would be unusual to get or more questions correct by guessing alone. Give your answer in the box above as a whole number. Submit Question Question 21 60/1 pt 0 3 # 99 0 Details The correct size of a nickel is 21.21 millimeters. Children of low- and high- income households were asked to draw a nickel of actual size. Based on that, the data can be summarized into the following table: Too Small | Too Large Total Low Income 15 25 40 High Income 24 11 35 Total 39 36 75 Based on this data: (give your answers to parts a-c as fractions, or decimals to at least 4 decimal places. Give your answer to part d as a whole number.) a) The proportion of all children that drew the nickel too small is: Assume that this proportion is true for ALL children (e.g. that this proportion applies to any group of children), and that the remainder of the questions in this section apply to selections from the population of ALL children. b) If 7 children are chosen, the probability that exactly 3 would draw the nickel too small is: c) If 7 children are chosen at random, the probability that at least one would draw the nickel too small is: d) If 120 children are chosen at random, it would be unusual if or more drew the nickel too small. (Assume unusual is more than 2 SD from the mean.) Submit