Let X: failure in machines in an 8 hrs shift have exponential distribution with 1.5 failures.
a) P(X = 2)
For 16 hours the failure rate is 1.5 * 2 = 3 failures that is
The pdf of exponential distribution is,
The probability that exactly 2 failures takes place is 0.0074
b) P(X more than medium value)
The standard deviation of exponential distribution is,
Medium value is nothing but median.
The median of exponential distribution is,
The distribution function of exponential distribution is,
Probability that number of failures in 8 hours exceed the medium value is 0.422367
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