Waiting Time The waiting time t (in minutes) for service in a store is exponentially distributed with a mean of 5 minutes.
(a) Find the probability density function for the random variable t.
(b) Find the probability that the waiting time is within one standard deviation of the mean.
(a)
To calculate: The probability density function for the random variable t, if the waiting time t (in minutes) is exponentially distributed with a mean of 5 minutes for service in a store.
Given information:
The waiting time t (in minutes) is exponentially distributed with a mean of 5 minutes for service in a store.
Formula used:
The exponential probability density function,
Here, an expected value is,
Calculation:
The provided time is t,
Consider a function as f with respect to t,
Use the formula of the exponential probability density function, the function will be,
To find the value of a use the formula
(b)
To calculate: The probability that the waiting time is within one standard deviation of the mean, if the waiting time t (in minutes) is exponentially distributed with a mean of 5 minutes for service in a store.
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