On the average, 7.8 cars arrive at the drive-up window of a bank every hour. Define the random variable x to be the number of cars arriving in any hour. (a) What is the appropriate probability distribution for x? Explain how x satisfies the properties of the distribution. O x is described by a uniform distribution because the probability of x occurrences is the same for all values of x. O x is described by a Poisson distribution because a Poisson distribution describes the probability of x occurrences of the event over n trials. O x is described by a binomial distribution because a binomial distribution describes the probability of x occurrences of the event over a time period. O x is described by a binomial distribution because a binomial distribution describes the probability of x occurrences of the event over n trials. O x is described by a Poisson distribution because a Poisson distribution describes the probability of x occurrences of the event over a time period. (b) Compute the probability that exactly 5 cars will arrive in the next hour. (Round your answer to four decimal places.) (c) Compute the probability that no more than 4 cars will arrive in the next hour. (Round your answer to four decimal places.)

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You may need to use the appropriate appendix table or technology to answer this question.

On the average, **7.8 cars** arrive at the drive-up window of a bank every hour. Define the random variable \( x \) to be the number of cars arriving in any hour.

(a) What is the appropriate probability distribution for \( x \)? Explain how \( x \) satisfies the properties of the distribution.

- ○ \( x \) is described by a uniform distribution because the probability of \( x \) occurrences is the same for all values of \( x \).
- ○ \( x \) is described by a Poisson distribution because a Poisson distribution describes the probability of \( x \) occurrences of the event over \( n \) trials.
- ○ \( x \) is described by a binomial distribution because a binomial distribution describes the probability of \( x \) occurrences of the event over a time period.
- ○ \( x \) is described by a binomial distribution because a binomial distribution describes the probability of \( x \) occurrences of the event over \( n \) trials.
- ● \( x \) is described by a Poisson distribution because a Poisson distribution describes the probability of \( x \) occurrences of the event over a time period.

(b) Compute the probability that **exactly 5 cars** will arrive in the next hour. (Round your answer to four decimal places.)

[Text Box for Answer]

(c) Compute the probability that **no more than 4 cars** will arrive in the next hour. (Round your answer to four decimal places.)

[Text Box for Answer]
Transcribed Image Text:You may need to use the appropriate appendix table or technology to answer this question. On the average, **7.8 cars** arrive at the drive-up window of a bank every hour. Define the random variable \( x \) to be the number of cars arriving in any hour. (a) What is the appropriate probability distribution for \( x \)? Explain how \( x \) satisfies the properties of the distribution. - ○ \( x \) is described by a uniform distribution because the probability of \( x \) occurrences is the same for all values of \( x \). - ○ \( x \) is described by a Poisson distribution because a Poisson distribution describes the probability of \( x \) occurrences of the event over \( n \) trials. - ○ \( x \) is described by a binomial distribution because a binomial distribution describes the probability of \( x \) occurrences of the event over a time period. - ○ \( x \) is described by a binomial distribution because a binomial distribution describes the probability of \( x \) occurrences of the event over \( n \) trials. - ● \( x \) is described by a Poisson distribution because a Poisson distribution describes the probability of \( x \) occurrences of the event over a time period. (b) Compute the probability that **exactly 5 cars** will arrive in the next hour. (Round your answer to four decimal places.) [Text Box for Answer] (c) Compute the probability that **no more than 4 cars** will arrive in the next hour. (Round your answer to four decimal places.) [Text Box for Answer]
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