Answer to Question #98385 in Statistics and Probability for debra gross

Question

the time taken to clean up a particular fast food outlet after it closes follows a normal distribution with a mean of 30 minutes and a standard deviation of 5 minutes.

a. what is the probability that the cleanup crew will complete the job in less than 20 minutes?
b. What is the probability that the cleanup crew will complete the job in more than 38 minutes?

Answer 1

Let $X=$ the time taken to clean up a particular fast food outlet after it closes in minutes:$X\sim N(\mu, \sigma^2)$

Then

$$Z={X-\mu \over \sigma}\sim N(0,1)$$

Given that $\mu=30\ minutes, \sigma=5 \ minutes$

a.

$$P(X<20)=P(Z<{20-30 \over 5})=P(Z<-2)\approx$$

$$\approx0.022750$$

 The probability that the cleanup crew will complete the job in less than 20 minutes is $0.0228$

b.

$$P(X>38)=1-P(X\leq38)=1-P(Z\leq{38-30 \over 5})=$$

$$=1-P(Z\leq1.6)\approx1-0.945201\approx0.0548$$

The probability that the cleanup crew will complete the job in more than 38 minutes is $0.0548$