Question

The modeling and solution of problems concerning motel reservation networks for motels were studied. Researchers defined a Type I call to be a call from a motel's computer terminal to the national reservation center. For a certain motel, the number, X, of Type 1 calls per hour has a Poisson distribution with parameter 1 = 1.2. Complete parts (a) through (e) below. .... a. Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be exactly two. The probability that exactly two Type 1 calls are made is (Round to three decimal places as needed.) b. Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be at most two. The probability that at most two Type 1 calls are made is (Round to three decimal places as needed.) c. Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be at least four. (Hint: Use the complementation rule.) The probability that at least four Type 1 calls are made is (Round to three decimal places as needed.) d. Find and interpret the mean of the random variable X. The mean is call(s) and therefore, there is/are V per hour from 7 to (Round to three decimal places as needed.) e. Find the standard deviation of the random variable X. The standard deviation is call(s). (Round to three decimal places as needed.)

Answer 1

The student's question pertains to the calculation of probabilities using the Poisson distribution for the number of Type 1 calls at a motel and related statistics such as mean and standard deviation.

Step-by-step explanation:

The questions provided are based on Poisson distribution and exponential distribution, two concepts from probability theory which are commonly used in the field of statistics. These types of problems are solved using specific formulas associated with the respective distributions. The Poisson distribution is often used to model the number of discrete events in a fixed interval of time or space when these events occur with a known constant mean rate and independently of the time since the last event. The exponential distribution is typically used to model the time between such events.

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• The probability that exactly two Type 1 calls are made in a period of one hour from a motel: P(X = 2).
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• The probability that at most two Type 1 calls are made in a period of one hour from a motel: P(X ≤ 2).
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• The probability that at least four Type 1 calls are made in a period of one hour from a motel: P(X ≥ 4).
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• The average number of calls per hour (the mean of the random variable X).
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• The standard deviation of the number of calls per hour (the standard deviation of the random variable X).