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Chapter 6: Q. 6.3 (page 436)
Let D be the difference in the number of puzzles solved by two randomly selected subjects in a 5-minute period. What is the standard deviation of D?
a. 0
b. 0.81
c. 0.9
d. 1.27
e. 1.8
(c) The standard deviation of D is 0.9
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Kids and toys In an experiment on the behavior of young children, each subject is placed in an area with five toys. Past experiments have shown that the probability distribution of the number X of toys played with by a randomly selected subject is as follows:
Part (a). Write the event 鈥渃hild plays with 5 toys鈥� in terms of X. Then find its probability.
Part (b). What鈥檚 the probability that a randomly selected subject plays with at most 3 toys?
Electronic circuit The design of an electronic circuit for a toaster calls for a ohm resistor and a -ohm resistor connected in series so that their resistances add. The components used are not perfectly uniform, so that the actual resistances vary independently according to Normal distributions. The resistance of -ohm resistors has mean ohms and standard deviation ohms, while that of -ohm resistors has mean 250 ohms and standard deviation 2.8ohms.
(a) What is the distribution of the total resistance of the two components in series?
(b) What is the probability that the total resistance
Skee Ball Ana is a dedicated Skee Ball player (see photo) who always rolls for the 50- point slot. The probability distribution of Ana鈥檚 score X on a randomly selected roll of the ball is shown here.
Part (a). Find Interpret this result.
Part (b). Express the event 鈥淎nna scores at most 20鈥� in terms of X. What is the probability of this event?
Auto emissions The amount of nitrogen oxides (NOX) present in the exhaust of a particular model of old car varies from car to car according to a Normal distribution with mean 1.4 grams per mile and standard deviation . Two randomly selected cars of this model are tested. One has of ; the other has . The test station attendant finds this difference in emissions between two similar cars surprising. If the NOX levels for two randomly chosen cars of this type are independent, find the probability that the difference is greater than or less than .
Life insurance A life insurance company sells a term insurance policy to 21-year-old males that pays \(100,000 if the insured dies within the next 5 years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of \)250 each year as payment for the insurance. The amount Y that the company earns on a randomly selected policy of this type is \(250 per year, less the \)100,000 that it must pay if the insured dies. Here is the probability distribution of Y:
(a) Explain why the company suffers a loss of $98,750 on such a policy if a client dies at age 25.
(b) Calculate the expected value of Y. Explain what this result means for the insurance company.
(c) Calculate the standard deviation of Y. Explain what this result means for the insurance company.
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