#46,54,58,62

A player receives one ti or the game for every 10 points Section 6.2 Exercises dent. selected roll. Fored. Define 1 = number of tickets Ana gets on a randomly 427 s a Normal What shape does the probability distribution of T have? by a Normal distribution with mean 8.5C and standard (b) Find the mean of T. deviation 2.25.C. Let Y = the temperature in the cabin at midnight on a randomly selected night in degrees Calculate the standard deviation of T. Fahrenheit (recall that F = (9/5)C + 32). $. Still waiting for the server? How does your web browser (a) Find the mean of Y. get a file from the Internet ? Your computer sends a request for the file to a web server, and the web server sends back (b) Calculate and interpret the standard deviation of Y. a response . Let Y = the amount of $3 use tax paint of time (in seconds) after (c) Find the probability that the midnight temperature in the start of an hour at which a randomly selec the cabin is less than 40F. al amount mly selected request is received by a particular web server. The probability 48. How much cereal? A company's single-serving cereal distribution of Y can be modeled by a uniform density boxes advertise 1.63 ounces of cereal. In fact, the of T. curve on the interval from 0 to 360 amount of cereal X in a randomly selected box can random variable W = Y/60. to 3600 seconds. Define the be modeled by a Normal distribution with a mean of (a) Explain what W represents. 1.70 ounces and a standard deviation of 0.03 ounce. Let Y = the excess amount of cereal beyond what's (b ) What probability distribution does W have? advertised in a randomly selected box, measured in grams (1 ounce = 28.35 grams). f hour 44. Where's the bus? Sally takes the same bus to work every e number morning . Let X = the amount of time ( in minutes) that (a) Find the mean of Y. the prob- she has to wait for the bus on a randomly selected day. The (b) Calculate and interpret the standard deviation of Y. = 3.87 probability distribution of X can be modeled by a uniform density curve on the interval from 0 minutes to 8 minutes. (c) Find the probability of getting at least 1 gram more cereal than advertised. Define the random variable V = 60X. (a) Explain what V represents. 49. Community college costs El Dorado Community g417 College has a main campus in the suburbs and a (b) What probability distribution does V have? downtown campus. The amount X spent on tuition Exercises 45 and 46 refer to the following setting. Ms. Hall gave randomly selected student at the main campus has m her class a 10-question multiple-choice quiz. Let X = the num- $732.50 and standard deviation $103. The amount ber of questions that a randomly selected student in the class Y spent on tuition by a randomly selected student at the downtown campus has mean $825 and standard answered correctly. The computer output gives information deviation $126.50. Suppose we randomly select one about the probability distribution of X. To determine each stu- time student from each of the two campuses. Calcu dent's grade on the quiz (out of 100), Ms. Hall will multiply and interpret the mean of the sum S = X + Y. his or her number of correct answers by 5 and then add 50. Let 50. Essay errors Typographical and spelling errors can G = the grade of a randomly chosen student in the class. either "nonword errors" or "word errors." A nonwor StDev Min Max error is not a real word, as when "the" is typed as "te Mean Median Q Q3 7.6 8.5 1.32 4 10 8 9 A word error is a real word, but not the right word, when "lose" is typed as "loose." When students are have? 45. Easy quiz to write a 250-word essay (without spell-checking) (a) Find the median of G. number of nonword errors X in a randomly selecte has mean 2.1 and standard deviation 1.136. The n (b) Find the interquartile range (IQR) of G. of word errors Y in the essay has mean 1.0 and star 10 46. More easy quiz deviation 1.0. Calculate and interpret the mean of a sum S = X+Y. lity la) Find the mean of G. 51. Study habits The Survey of Study Habits and d (b) Find the range of G. (SSHA) is a psychological test that measures ac 47. Too cool at the cabin? During the winter months, the motivation and study habits. The SSHA score 945 temperatures at the Starneses' Colorado cabin can stay randomly selected female student at a large un well below freezing (32 F or O'C) for weeks at a time. has mean 120 and standard deviation 28, and To prevent the pipes from freezing, Mrs. Starnes sets the SSHA score M of a randomly selected male st thermostat at 50 F. She also buys a digital thermometer the university has mean 105 and standard devi that records the indoor temperature each night at Suppose we select one male student and one midnight. Unfortunately, the thermometer is programmed student at random from this university and gi to measure the temperature in degrees Celsius. Based on the SSHA test. Calculate and interpret the m several years' worth of data, the temperature T in the cabin difference D = F - M in their scores. at midnight on a randomly selected night can be modeledRANDOM VARIABLES AND PROBABILITY DISTRIBUTION 428 CHAPTER 6 59. Study habits Refer to Exercise 51. 52. Commuting to work Sule's job is just a few bus stops (a) Assume that F and M are independent random away from his house. While it can be faster to take variables. Explain what this means in context. the bus to work than to walk, the travel time is more variable due to traffic. The commute time B if Sule (b) Calculate and interpret the standard deviation of the takes the bus to work on a randomly selected day has difference D = F - M in their scores. mean 12 minutes and standard deviation 4 minutes. (c) From the information given, can you find the The commute time W if Sule walks to work on a randomly selected day has mean 16 minutes and probability that the randomly selected female student standard deviation 1 minute. Calculate and interpret has a higher SSHA score than the randomly selected male student? Explain why or why not. the mean of the difference D = B - W in the time it would take Sule to get to work on a randomly 60. Commuting to work Refer to Exercise 52. selected day. (a) Assume that B and W are independent random 53. Community college costs Refer to Exercise 49. At variables. Explain what this means in context. the main campus, full-time students pay $50 per unit. At the downtown campus, full-time students pay $55 (b) Calculate and interpret the standard deviation of the per unit. Find the mean of the difference D (Main - difference D (Bus - Walk) in the time it would take Downtown) in the number of units that the two Sule to get to work on a randomly selected day. randomly selected students take. (c) From the information given, can you find the 54. Essay scores Refer to Exercise 50. An English probability that it will take Sule longer to get to work professor deducts 3 points from a student's essay score on the bus than if he walks on a randomly selected for each nonword error and 2 points for each word day? Explain why or why not. error. Find the mean of the total score deductions T for a randomly selected essay. 61. Community college costs Refer to Exercise 49. Note that X and Y are independent random variables 55. Rainy days Imagine that we randomly select a day because the two students are randomly selected from from the past 10 years. Let X be the recorded rainfall each of the campuses. At the main campus, full-time on this date at the airport in Orlando, Florida, and Y be students pay $50 per unit. At the downtown campus, the recorded rainfall on this date at Disney World just full-time students pay $55 per unit. Suppose we outside Orlando. Suppose that you know the means /x randomly select one full-time student from each of and My and the variances ox and or of both variables. the two campuses. Find the standard deviation of the (a) Can we calculate the mean of the total rainfall X + Y difference D (Main - Downtown) in the number of to be ux + My? Explain your answer. units that the two randomly selected students take. (b) Can we calculate the variance of the total rainfall to be 62. Essay scores Refer to Exercise 50. Assume that the Ox + or? Explain your answer. number of nonword errors X and word errors Y in 56. His and her earnings Researchers randomly select a a randomly selected essay are independent random married couple in which both spouses are employed. variables. An English professor deducts 3 points from a Let X be the income of the husband and Y be the student's essay score for each nonword error and 2 points income of the wife. Suppose that you know the for each word error. Find the standard deviation of the means ux and My and the variances off and or of both total score deductions T for a randomly selected essay. variables. Exercises 63 and 64 refer to the following setting. In Exercise (a) Can we calculate the mean of the total income X + Y 17 of Section 6.1, we examined the probability distribution to be ux + My? Explain your answer. of the random variable X = the amount a life insurance (b) Can we calculate the variance of the total income to be company earns on a randomly chosen 5-year term life policy. ox + or? Explain your answer. Calculations reveal that ux = $303.35 and ox = $9707.57. 57. Community college costs Refer to Exercise 49. 63. Life insurance The risk of insuring one person's life g 421 Note that X and Y are independent random variables is reduced if we insure many people. Suppose that we because the two students are randomly selected from randomly select two insured 21-year-old males, and that each of the campuses. Calculate and interpret the their ages at death are independent. If X, and X2 are the standard deviation of the sum S = X + Y. insurer's income from the two insurance policies, the 58. Essay errors Refer to Exercise 50. Assume that the insurer's average income Won the two policies is number of non-word errors X and word errors Y in W = XI+ X 2 a randomly selected essay are independent random Find the mean and standard deviation of W. (You see 2 variables. Calculate and interpret the standard deviation of the sum S = X + Y. that the mean income is the same as for a single policy. but the standard deviation is less.)