Over a one-year period, it is observed that on approximately five percent of the days, a particular public telephone in a remote part of an airport is not used at all. On ninety-five percent of the days it is used, but the number of users is not known. Make a reasonable estimate of the average number of users per day of that particular phone.
To estimate the average number of users per day for the particular public telephone, we need to make some assumptions based on the information provided.
We know that on approximately five percent of the days, the phone is not used at all. This means that there are 365 x 0.05 = 18.25 days in a year when the phone is not used.
On the remaining 365 - 18.25 = 346.75 days, the phone is used. However, we don't know the exact number of users on these days.
Since we only have information about the percentage of days the phone is not used, we can assume that the distribution of users per day follows a Poisson distribution, which is a reasonable assumption for situations like this.
To estimate the average number of users per day, we can use the formula for the mean of a Poisson distribution, which is equal to the variance. The formula for the mean of a Poisson distribution is given by λ, where λ is the rate parameter.
The rate parameter (λ) can be calculated as the number of users per day multiplied by the probability of a day being used.
Let's assume x is the average number of users per day. So, on 346.75 days, we have x users on each day. This gives us a total of 346.75 * x users over the course of the year.
Since we don't know the exact number of users, we need to estimate it. Let's take an educated guess that x is around 10, for example.
With x = 10, the rate parameter λ would be λ = x * (0.95) = 10 * 0.95 = 9.5.
Therefore, our estimate for the average number of users per day would be around 9.5 users per day for that particular public telephone.