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Chapter 6: Q. 90 (page 405)
90. Normal approximation To use a Normal distribution to approximate binomial probabilities, why do we require that both and be at least ?
Both and have different shapes, if the provided condition is not valid.
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50. Checking independence For each of the following situations, would you expect the random variables and to be independent? Explain your answers.
(a)is the rainfall (in inches) on November of this year, and is the rainfall at the same location on November of next year.
(b) is the amount of rainfall today, and is the rainfall at the same location tomorrow.
(c) is today's rainfall at the airport in Orlando, Florida, and is today's rainfall at Disney World just outside Orlando.
Binomial setting? A binomial distribution will be approximately correct as a model for one of these two settings and not for the other. Explain why by briefly discussing both settings. (a) When an opinion poll calls residential telephone numbers at random, only of the calls reach a person. You watch the random digit dialing machine make calls. is the number that reaches a person
(b) When an opinion poll calls residential telephone numbers at random, only of the calls reach a live person. You watch the random digit dialing machine make calls. is the number of calls until the first live person answers
23. ITBS scores The Normal distribution with mean and standard deviation is a good description of the Iowa Test of Basic Skills (ITBS) vocabulary scores of seventh-grade students in Gary, Indiana. Call the score of a randomly chosen student for short. Find and interpret the result. Follow the four-step process.
Buying stock You purchase a hot stock for . The stock either gains or loses each day, each with probability . Its returns on consecutive days are independent of each other. You plan to sell the stock after two days.
(a) What are the possible values of the stock after two days, and what is the probability for each value? What is the probability that the stock is worth more after two days than the you paid for it?
(b) What is the mean value of the stock after two days?
(Comment: You see that these two criteria give different answers to the question "Should I invest?")
83. Random digit dialing Refer to Exercise 81. Let the number of calls that don鈥檛 reach a live person.
(a) Find the mean of . How is it related to the mean of ? Explain why this makes sense.
(b) Find the standard deviation of How is it related to the standard deviation of ? Explain why this makes sense
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