During weekday mid-morning hours, phone calls arrive at a motel chain\'s 800 num

Question

During weekday mid-morning hours, phone calls arrive at a motel chain's 800 number reservation center at the rate of 60 per hour. The probability of a call arriving is the same during any two periods of equal length during these hours. The arrival or nonarrival of a call in any time period is independent of the arrival or non-arrival of a call in any other time period of equal length during these hours. What is the probability of at least five calls in a 10-minute period during weekday mid-morning hours?

Explanation / Answer

During weekday mid-morning hours, phone calls arrive at a motel chain's 800 number reservation center at the rate of 60 per hour

The probability of a call arriving is the same during any two periods of equal length during these hours. The arrival or nonarrival of a call in any time period is independent of the arrival or non-arrival of a call in any other time period of equal length during these hours.

Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is mostly of mathematical interest and not directly relevant to statistics. Moreover, many topics in statistics are independent of probability theory.

Mathematically, the probability that an event will occur is expressed as a number between 0 and 1. Notationally, the probability of event A is represented by P(A).

In a statistical experiment, the sum of probabilities for all possible outcomes is equal to one. This means, for example, that if an experiment can have three possible outcomes (A, B, and C), then P(A) + P(B) + P(C) = 1.

How to Compute Probability: Equally Likely Outcomes

Sometimes, a statistical experiment can have n possible outcomes, each of which is equally likely. Suppose a subset of r outcomes are classified as "successful" outcomes.

The probability that the experiment results in a successful outcome (S) is:

P(S) = ( Number of successful outcomes ) / ( Total number of equally likely outcomes ) = r / n

Consider the following experiment. An urn has 10 marbles. Two marbles are red, three are green, and five are blue. If an experimenter randomly selects 1 marble from the urn, what is the probability that it will be green?

In this experiment, there are 10 equally likely outcomes, three of which are green marbles. Therefore, the probability of choosing a green marble is 3/10 or 0.30.

Then the probability of at least five calls in a 10-minute period during weekday mid-morning hours is 0.9707

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