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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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14. . Life insurance A life insurance company sells a term insurance policy to a -year-old male that pays if the insured dies within the next years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of each year a payment for the insurance. The amount that the company earns on this policy is per year, less the that it must pay if the insured dies. Here is a partially completed table that shows information about risk of mortality and the values of profit earned by the company:
(a) Copy the table onto your paper. Fill in the missing values of .
(b) Find the missing probability. Show your work.
(c) Calculate the mean .Interpret this value in context
To collect information such as passwords, online criminals use 鈥渟poofing鈥� to direct Internet users to fraudulent Web sites. In one study of Internet fraud, students were warned about spoofing and then asked to log in to their university account starting from the university鈥檚 home page. In some cases, the login link led to the genuine dialog box. In others, the box looked genuine but in fact was linked to a different site that recorded the ID and password the student entered. An alert student could detect the fraud by looking at the true Internet address displayed in the browser status bar below the window, but most just entered their ID and password. Is this study an experiment? Why? What are the explanatory and response variables?
To introduce her class to binomial distributions, Mrs. Desai gives a -item, multiple-choice quiz. The catch is, that students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class.
Let the number of Patti's correct guesses.
To get a passing score on the quiz, a student must guess correctly at least times. Would you be surprised if Patti earned a passing score? Compute an appropriate probability to support your answer.
51. His and her earnings A study of working couples measures the income of the husband and the income of the wife in a large number of couples in which both partners are employed. Suppose that you knew the means and and the variances and of both variables in the population.
(a) Is it reasonable to take the mean of the total income to be ? Explain your answer.
(b) Is it reasonable to take the variance of the total income to be ? Explain your answer.
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?")
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