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_ m 5-1HMWk'an0tO X 6 9 O Q j https://www.webassign.net/web/Student/AssignmentResp... A\" {3 0i 6'\" 5:: g . else. : 3. [0.5\" Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 5.1.006. MY NOTES ASK YOUR TEACHER Consider the probability distribution of a random variable x. 15 the expected value of the distribution necessarily one of the possible values of x? No. The expected value can be a value different from the exact value of x. O Yes. The expected value can never be a value from the exact value of x. O No. The expected value will never be one of its possible values of x. O Yes. The expected value must always be one of its possible values of x. I Explain or give an example. I This answer has not been graded yet. Need Help? i v ,0 Type here to search e _ m 5-1Hka'lntht0 X 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 Ci 6'\" 5:: g . {3 I {'5 . What is the age distribution of promotion-sensitive shoppers? A supermarket super shopper is dened as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. 1828 2939 4050 5161 62 and over 23 34 45 56 67 6% 4 1 % 25 % 1 3 % 1 5% IE USE SA For the 62and-over group, use the midpoint 67 years. I (a) Using the age midpoints x and the percentage of super shoppers, do we have a valid probability distribution? Explain. Yes. The events are distinct and the probabilities sum to 1. 0 Yes. The events are distinct and the probabilities do not sum to 1. 0 Yes. The events are indistinct and the probabilities sum to less than 1. O No. The events are indistinct and the probabilities sum to more than 1. O No. The events are distinct and the probabilities sum to 1. I (b) Use a histogram to graph the probability distribution of part (3). (Because the data table has summarized the data into categories, use SALT to create a bar chart.) ,0 Type here to search Financial InformationX VA 5.1 Hmwk - Intro to X y! Consider the probal x Connect X *Course Hero X G Grammarly X + X https://www.webassign.net/web/Student/Assignment-Resp... A sd . . . 40 40- 30- 30- Supr Shpprs 20 Supr Shpprs 20 10 10 23 34 45 56 67 23 34 45 56 67 Age O Age O (c) Compute the expected age u of a super shopper. (Round your answer to two decimal places.) H = 41.70 X yr (d) Compute the standard deviation o for ages of super shoppers. (Round your answer to two decimal places.) 0 = yr Need Help? Read It Master It Type here to search O E O W 45OF 4:33 AM 2/10/2022- m 51 Hkai lntm t0 RND Vaflabl' X 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 Ci 6'\" 5:: g . {3 l {'5 . What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Suppose we have the following information. Note: In 1851 there were 25,466 nurses in Great Britain. 2029 3039 4049 50- 59 6069 7079 80+ 24.5 34.5 44.5 54.5 64.5 74.5 84.5 5.4% 9.2% 19.1% 29.2% 25.5% 10.0% 1.6% [a USE SALT (a) Using the age midpoints x and the percent of nurses, do we have a valid probability distribution? Explain. O Yes. The events are distinct and the probabilities do not sum to 1. O No. The evenis are indistinct and the probabilities sum to 1. O No. The events are indistinct and the probabilities do not sum to 1. r I (b) Use a histogram to graph the probability distribution in part (a). (Because the data table has summarized the data into categories, use SALT to create a bar chart.) (9 Yes. The events are distinct and the probabilities sum to 1. 25 25 20 20 l of Nurses I5 I of Nurses 15 lo 10 ,0 Type here to search VA 5.1 Hmwk - Intro to RND Variable X + X -> https://www.webassign.net/web/Student/Assignment-Resp... A sd Age O Ag O 25 25 20- 20 $ of Nurses 15 of Nurses 15 10 10 5 24.5 34.5 44.5 54.5 64.5 74.5 84.5 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Age Age O (c) Find the probability that a British nurse selected at random in 1851 would be 60 years of age or older. (Round your answer to three decimal places.) (d) Compute the expected age u of a British nurse contemporary to Florence Nightingale. (Round your answer to two decimal places.) yr (e) Compute the standard deviation o for ages of nurses shown in the distribution. (Round your answer to two decimal places.) yr Need Help? Read It Type here to search O S ( O O W 45OF 4:34 AM 2/10/2022- m 51 Hkai lntm t0 RND Vaflabll X 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 Oi Eh 5:: g . {3 l {'5 . USA Today reported that approximately 25% of all state prison inmates released on parole become repeat offenders while on parole. Suppose the parole board is examining ve prisoners up for parole. Let X = number of prisoners out of ve on parole who become repeat offenders. 0 1 2 3 4 5 0.227 0. 366 0.209 0.168 0.029 0.001 (a) Find the probability that one or more of the ve parolees will be repeat offenders. (Round your answer to three decimal places.) :1 How does this number relate to the probability that none of the parolees will be repeat offenders? O These probabilities are not related to each other. 0 These probabilities are the same. O This is the complement of the probability of no repeat offenders. O This is ve times the probability of no repeat offenders. O This is twice the probability of no repeat offenders. (b) Find the probability that two or more of the ve parolees will be repeat offenders. (Round your answer to three decimal places.) (c) Find the probability that four or more of the ve parolees will be repeat offenders. (Round your answer to three decimal places.) I :1 (d) Compute pi, the expected number of repeat offenders out of five. (Round your answer to three decimal places.) (e) Compute a, the standard deviation of the number of repeat offenders out of ve. (Round your answer to two decimal places.) ,0 Type here to search - m 51 Hkai lntm t0 RND Vaflabll X 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 GI Eh 5:: g . {3 l {'5 . Jim is a 60-year-old Anglo male in reasonably good health. He wants to take out a $50,000 term (that is, straight death benet) life insurance policy until he is 65. The policy will expire on his 65th birthday. The probability of death in a given year is provided by the Vital Statistics Section of the Statistical Abstract of the United States (116th Edition). 60 61 62 63 64 0.01084 0.01444 0.01657 0.01954 0.02221 Jim is applying to Big Rock Insurance Company for his term insurance policy. (a) What is the probability that Jim will die in his 60th year? (Enter your answer to ve decimal places.) :1 Using this probability and the $50,000 death benet, what is the expected cost to Big Rock Insurance? (Round your answer to two decimal places.) $:l (b) Repeat part (a) for years 61, 62, 63, and 64. (Round your answers to two decimal places.) Year Expected Cost 61 .S 62 as: 62 $:] 64 9.: What would be the total expected cost to Big Rock Insurance over the years 60 through 64? (Round your answer to two decimal places.) $l:l (c) If Big Rock Insurance wants to make a prot of $700 above the expected total cost paid out for Jim's death, how much should it charge for the policy? (Round your answer to two decimal places.) 5F: (d) If Big Rock Insurance Company charges $5000 for the policy, how much prot does the company expect to make? (Round your answer to two decimal places.) $ v ,0 Type here to search e - m 51 Hkai lntm t0 RND Valiabl' X 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 Fl 6'\" \"I g . {3 I {'5 . l " ' g] IJ'lJ'lJ A A computer repair shop has two work centers. The rst center examines the computer to see what is wrong, and the second center repairs the computer: Let x1 and x2 be random variables representing the lengths of time in minutes to examine a computer (x1) and to repair a computer (x2). Assume X and X2 are independent random 1 variables. Longterm history has shown the following times. Examine computer, x1: :11 = 28.0 minutes; J1 = 7.5 minutes Repair computer, x2: '12 = 91.4 minutes; 02 = 14.3 minutes (a) Let W = x1 + X2 be a random variable representing the total time to examine and repair the computer. Compute the mean, variance, and standard deviation of W. (Round your answers to two decimal places.) u (b) Suppose it costs $1.50 per minute to examine the computer and $2.75 per minute to repair the computer. Then W = 1.50X1 + 2.75):2 is a random variable representing the service charges (without parts). Compute the mean, variance, and standard deviation of W. (Round your answers to two decimal places.) (c) The shop charges a at rate of $1.50 per minute to examine the computer, and if no repairs are ordered, there is also an additional $50 service charge. Let L = 1.5x1 + 50. Compute the mean, variance, and standard deviation of L. (Round your answers to two decimal places.) y I (T2 0 ,0 Type here to search - m 51 Hkai lntm t0 RND Vaflabl X 6 9 O Q Q https://www.webassign.net/web/Student/AssignmentResp... A\" {3 Fl Eh \"l g . {3 l {'5 . ll lJ_Ll_ll A Insurance companies know the risk of insurance is greatly reduced if the company insures not just one person, but many people. How does this work? Let x be a random variable representing the expectation of life in years for a 25-year-old male (i.e., number of years until death). Then the mean and standard deviation ofx are p = 48.7 years and a = 12.5 years (Vital Statistics Section of the Statistical Abstract of the United States, 116th Edition). Suppose Big Rock Insurance Company has sold life insurance policies to Joel and David. Both are 25 years old, unrelated, live in different states, and have about the same health record. Let X1 and x2 be random variables representing Joel's and David's life expectancies. It is reasonable to assume x1 and x2 are independent. Joel, X1: 48.7; \"1 = 12.5 David, X2: 48.7; crl = 12.5 If life expectancy can be predicted with more accuracy, Big Rock will have less risk in its insurance business. Risk in this case is measured by a (larger 0 means more risk). (a) The average life expectancy for Joel and David is W = 0.5x1 + 0.5x2. Compute the mean, variance, and standard deviation of W. (Use 2 decimal places.) (b) Compare the mean life expectancy for a single policy (X1) with that for two policies (W). O The means are the same. O The mean of W is larger. 0 The mean of W is smaller. (c) Compare the standard deviation of the life expectancy for a single policy (x1) with that for two policies (W). O The standard deviations are the same. 0 The standard deviation of W is smaller. O The standard deviation of W is larger: I Need Help? i i - ,0 Type here to search