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Answer:
Probability that the wait time is greater than 37 minutes is 0.3474.
Step-by-step explanation:
We are given that the random variable X is known to be exponentially distributed and X be the waiting time for a car to pass by on a country road, where X has an average value of 35 minutes.
<u><em>Let X = waiting time for a car to pass by on a country road</em></u>
The probability distribution function of exponential distribution is given by;
where,
= parameter of distribution.
Now, the mean of exponential distribution is = which is given to us as 35 minutes that means
.
So, X ~ Exp( )
Also, we know that Cumulative distribution function (CDF) of Exponential distribution is given as;
, x > 0
Now, Probability that the wait time is greater than 37 minutes is given by = P(X > 37 min) = 1 - P(X 37 min)
P(X 37 min) =
{Using CDF}
= 1 - 0.3474 = 0.6525
So, P(X > 37 min) = 1 - 0.6525 = 0.3474
Therefore, probability that the wait time is greater than 37 minutes is 0.3474.