Question

On average, 15 minutes elapse between discoveries of fraudulent corporate tax returns in a certain IRS office. What is the probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered

Answer 1

The probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered=0.1353

Explanation:

We are given that

`\beta=15`

We have to find the probability that more that 30 minutes will elapse before the next fraudulent corporate tax return is discovered.

Using exponential distribution

`P(X> x)=e^{-(x)/(\beta)}`

The probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered

`=P(x>30)=e^{-(30)/(15)}`

The probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered

`P(x>30)=0.1353`

Hence, the probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered=0.1353