suppose that the wait time at the bank is uniformly distributed in the interval 4-min-8min find the probability that a randomly selected customer has to wait longer than 6.5 minutes
here the inter arrival time t~unif(4,8)
the for the prob. that there will be watting > 6.5 mint = intgral(from 6.5 to 8 mint of 1/(8-4) ) = .0375
To find the probability that a randomly selected customer has to wait longer than 6.5 minutes, you need to calculate the area under the probability density function (PDF) curve for the uniform distribution beyond 6.5 minutes.
In a uniform distribution, the probability density function is constant within a certain range. In this case, the range is from 4 minutes to 8 minutes, and the PDF value is 1/(8 - 4) = 1/4 within this range.
To find the probability beyond 6.5 minutes, you need to calculate the area under the PDF curve from 6.5 minutes to 8 minutes.
The length of this interval is 8 - 6.5 = 1.5 minutes.
To find the probability, you can use the formula:
Probability = (length of interval) * (PDF value)
Therefore, the probability that a randomly selected customer has to wait longer than 6.5 minutes is:
Probability = 1.5 minutes * (1/4) = 0.375 or 37.5%
So, there is a 37.5% chance that a randomly selected customer will have to wait longer than 6.5 minutes at the bank.