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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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Rotter Partners is planning a major investment. The amount of profit (in millions of dollars) is uncertain, but an estimate gives the following probability distribution:
Based on this estimate, and
Rotter Partners owes its lender a fee of plus of the profits . So the firm actually retains from the investment. Find the mean and standard deviation of the amount that the firm actually retains from the investment.
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?
A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let = the number of cars sold and = the number of cars leased during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distributions of and are as follows:
顿别铿乶别
Find and interpret .
A housing company builds houses with two-car garages. What percent of households have more cars than the garage can hold? (a)
(b)
(c)
(d)
(e)
Exercises 47 and 48 refer to the following setting. Two independent random variables and have the probability distributions, means, and standard deviations shown.
48. Difference Let the random variable .
(a) Find all possible values of D. Compute the probability that takes each of these values. Summarize the probability distribution of in a table.
(b) Show that the mean of is equal to.
(c) Confirm that the variance of is equal to .Find all possible values of . Compute the probability that takes each of these values. Summarize the probability distribution of in a table.
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