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Chapter 6: Q. 106 (page 431)
Large Counts condition To use a Normal distribution to approximate binomial probabilities, why do we require that both and be a t least ?
the shape of binomial distribution to normal distribution n p and n p 10 is used.
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Auto emissions The amount of nitrogen oxides {NOX}) present in the exhaust of a particular type of car varies from car to car according to a Normal distribution with mean grams per mile (g/mi) and standard deviation . Two randomly selected cars of this type are tested. One has of NOX; 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 at least as large as the value the attendant observed.follow the four-step process.
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, crème, 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?
In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p ?
a.
b.
c.
d.
e.
Long or short? Put the names of all the students in your statistics class in a hat. Mix up the names, and draw 4 without looking. Let X = the number whose last names have more than six letters.
Red light! Pedro drives the same route to work on Monday through Friday. His route includes one traffic light. According to the local traffic department, there is a chance that the light will be red on a randomly selected work day. Suppose we choose 10 of Pedro's work days at random and let the number of times that the light is red.
a. Explain why is a binomial random variable.
b. Find the probability that the light is red on exactly 7 days.
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