A review of the service call records of Paul’s Plumbing indicates that the time

Question

A review of the service call records of Paul’s Plumbing indicates that the time taken for a service call can be represented by a normal distribution with mean 50 minutes and standard deviation 10 minutes. What is the probability that a service call takes more than 35 minutes? (Be sure to indicate the relevant Z-score for the problem). What is the probability that a service call takes less than an hour? (Be sure to indicate the relevant Z-score for the problem). A plumber is scheduled to make 3 calls in a morning. The times taken for each call are independent of one another. What is the probability that all 3 of the calls will take more than one hour?

Explanation / Answer

1)here probability that a service call takes more than 35 minutes =P(X>35)=1-P(X<35)=1-P(Z<(35-50)/10)

=1=P(Z<-1.5) =1-0.0668 =0.9332

2)

probability that a service call takes less than an hour =P(X<60)=P(Z<(60-50)/10)=P(Z<1)=0.8413

3)

probability that all 3 of the calls will take more than one hour =(1-0.8413)3 =0.0040

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