QUESTION 1 10 points Save Answer At Cape College, the business students run an investment club. Each fall they create investment portfolios in multiples of $1000 each. Records from the past several years show the following probabilities of profits (rounded to the nearest $50). In the table below, x = profit per $1000 investment, and P(x) is the probability of earning that profit. X 10 50 100 150 200 P( x 0.15 0.35 0.25 0.20 0.05 Part a: Do the data represent a probability distribution? If so, answer the following questions. If not, type n/a in each blank. Part b: What is the probability that investors will earn at least $150? Part c: What is the probability that investors will earn no less than $50? QUESTION 2 10 points Save Answer A blindfolded marksman hits his target 3 out of 4 times. He fires five shots. The results are shown in the table below, where x represents the number of shots hitting the target and P(x) represents the probability. The following table gives part of the probability distribution for x. 14 5 P( x) 0.001 0.015 0.088 0.395 0.237 Part a: Complete the table. Part b: What is the probability that he hits the target at least 4 times? Part c: What is the probability that he hits the target fewer than 2 times? QUESTION 3 10 points Save Answer A local taxicab company is interested in the number of pieces of luggage a cab carries on a taxi run. A random sample gave the following information, where x is the number of pieces of luggage and P(x) represents the probability that a passenger will have that number of bags. X 10 1 2 3 4 P X) 0.05 0.21 0.29 0.18 0.17 Part a: Do the data represent a probability distribution? If so, answer the following questions. If not, type n/a in each blank. Part b: What is the probability that a passenger has no more than 1 bag? Part c: What is the probability that a passenger has no more than 3 bags? QUESTION 4 10 points Save Answer Patients are asked after surgery about whether or not they have pain. A random sample of 5 patients is surveyed. In the table below, x = number of people who have pain and P(x) is the probability that x people will have pain. The following table gives part of the probability distribution for x. 3 4 5 P( x) 0.1 0.2 0.3 0.3 Part a: Complete the table. Part b: What is the probability that patients' pain levels are at least 4? Part c: What is the probability that patients' pain levels are at most 3? QUESTION 5 10 points Save Answer A franchise chain of small grocery stores has kept records of the number of bad checks passed in its stores. They used the data to get a probability distribution for the number of bad checks passed in a store each week. In the table below, x = number of bad checks and P(x) is the probability that x bad checks will be passed in a week. X P( x 0.3 0.3 0.2 0.1 0.1 2 4 Part a: Do the data represent a probability distribution? . If so, answer the following questions. If not, type n/a in each blank. Part b: What is the probability that 2 or more bad checks will be passed in a week? Part c: What is the probability that no more than 3 bad checks will be passed in a week?QUESTION 6 10 points Save Answer The Young Fun Company operates a national toy store chain that relies heavily on the size of the child population, and research is being conducted to learn more about the number of children in families. In the accompanying table, x represents the number of children in families. 3 P x 0.48 0.21 0.19 0.08 Part a: Do the data represent a probability distribution? If so, answer the following questions. If not, type n/a in each blank. Part b: What is the probability that a family has fewer than 2 children? Part c: What is the probability that a family has no children? QUESTION 7 10 points Save Answer United Airlines flight 470 from Denver to St. Louis has an on-time performance represented in the table. In the probability distribution below, x = the number of on-time flights and P(x) = the probability for 4 independent flights. Assume the data represent a probability distribution. Complete the table. X 10 1 3 0.026 0.345 0.154 0.129 What is the mean of the data? To three decimal places, what is the standard deviation of the data? QUESTION 8 10 points Save Answer Car headlight manufacturers are concerned about failure rates. One headlight failure is an inconvenience, but if both lights fail you can't drive at night. The following table shows the probabilility of headlight failure, where x is the number of headlights that fail and P(x) represents the corresponding probability. Assume the data represent a probability distribution. What is the mean and standard deviation of the data? To P( X) 0.96 0.036 0.004 OH = 0.44, 0 = .05 PH = 0.044, o = 0.22 Pu = 1.5, 0 = 0.5 J = 4.4, 0 = 2.2 QUESTION 9 10 points Save Answer A blindfolded marksman hits his target 3 out of 4 times. He fires five shots. The results are shown in the table below, where x represents the number of shots hitting the target and P(x) represents the probability. Assume the data represent a probability distribution and determine the mean and standard deviation to three decimal places. X TO P X 0.001 0.015 0.088 0.264 0.395 0.237 H = QUESTION 10 10 points Save Answer The Young Fun Company operates a national toy store chain that relies heavily on the size of the child population, and research is being conducted to learn more about the number of children in families. In the accompanying table, x represents the number of children in families. Assume the data represent a probability distribution. X 10 1 2 3 4 P x 0.48 0.21 0.19 0.08 0.04 What is the mean of the data? To two decimal places, what is the standard deviation of the data