Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive-thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability that it takes less than one minute to fill an order

For this case we want to find this probability:

And we can use the cumulative distribution given by:

And replacing we got:

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

Solution to the problem

For this case we can define the random variable X= "how long it took customers to receive their order at the drive-thru"

And the distribution for X is given by:

For this case we want to find this probability:

And we can use the cumulative distribution given by:

And replacing we got:

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step-by-step explanation:

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value