SUPPLEMENTARY EXERCISES for ... - WH Freeman

Section 4 35Number of toys x i 0 1 2 3 4 5Probability p i 0.03 0.16 0.30 0.23 0.17 0.11Calculate the mean µ X and the standard deviation σ X .S4.28 The academic motivation and study habits of female students as a group are better thanthose of males. The Survey of Study Habits and Attitudes (SSHA) is a psychological test thatmeasures these factors. The distribution of SSHA scores among the women at a college has mean120 and standard deviation 28, and the distribution of scores among men students has mean105 and standard deviation 35. You select a single male student and a single female student atrandom and give them the SSHA test.(a) Explain why it is reasonable to assume that the scores of the two students are independent.(b) What are the mean and standard deviation of the difference (female minus male) of theirscores?(c) From the information given, can you find the probability that the woman chosen scoreshigher than the man? If so, find this probability. If not, explain why you cannot.S4.29 The psychologist Amos Tversky did many studies of our perception of chance behavior.In its obituary of Tversky (June 6, 1996), the New York Times cited the following example.(a) Tversky asked subjects to choose between two public health programs that affect 600 people.One has probability 1/2 of saving all 600 and probability 1/2 that all 600 will die. The otheris guaranteed to save exactly 400 of the 600 people. Find the mean number of people saved bythe first program.(b) Tversky then offered a different choice. One program has probability 1/2 of saving all 600and probability 1/2 of losing all 600, while the other will definitely lose exactly 200 lives. Whatis the difference between this choice and that in (a)?(c) Given option (a), most subjects choose the second program. Given option (b), most subjectschoose the first program. Do the subjects appear to use means in making their decisions? Whydo you think their choices differed in the two cases?S4.30 The original simple form of the Connecticut state lottery (ignoring a few gimmicks)awarded the following prizes for each 100,000 tickets sold. The winners were chosen by drawingtickets at random.1 $5000 prize18 $200 prizes120 $25 prizes270 $20 prizesIf you hold one ticket in this lottery, what is your probability of winning anything? What is themean amount of your winnings?S4.31 The number of offspring produced by a female Asian stochastic beetle is random, with thispattern: 20% of females die without female offspring, 30% have one female offspring, and 50%have two female offspring. Females of the benign boiler beetle have this reproductive pattern:40% die without female offspring, 40% have one female offspring, and 20% have two femaleoffspring.(a) Find the mean number of female offspring for each species of beetles.