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Chapter 6: Q. 105 (page 430)
condition To use a binomial distribution to approximate the count of successes in an SRS, why do we require that the sample size n be less than of the population size ?
The sample size n must be smaller than 10% of the population size N.
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Skee Ball Refer to Exercise 4. Make a histogram of the probability distribution. Describe its shape
Airport security The Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check before boarding. One such flight had 76 passengers- 12 in first class and 64 in coach class. Some passengers were surprised when none of the 10 passengers chosen for screening were seated in first class. Should we use a binomial distribution to approximate this probability? Justify your answer.
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
The time it takes Hattan to drive to work on a randomly selected day follows a distribution that is approximately Normal with mean minutes and standard deviation minutes. Once he parks his car in his reserved space, it takes more minutes for him to walk to his office. Let the total time it takes Hattan to reach his office on a randomly selected day, so . Describe the shape, center, and variability of the probability distribution of .
The last kiss Do people have a preference for the last thing they taste?
Researchers at the University of Michigan designed a study to find out. The researchers gave 22 students five different Hershey's Kisses (milk chocolate, dark chocolate, cr猫me, caramel, and almond) in random order and asked the student to rate each one. Participants were not told how many Kisses they would be tasting. However, when the 5th and final Kiss was presented, participants were told that it would be their last one. Assume that the participants in the study don't have a special preference for the last thing they taste. That is, assume that the probability a person would prefer the last Kiss tasted is .
a. Find the probability that 14 or more students would prefer the last Kiss tasted.
b. Of the 22 students, 14 gave the final Kiss the highest rating. Does this give convincing evidence that the participants have a preference for the last thing they taste?
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