A statistical consultant knows from past experience that the amount of time that

Question

A statistical consultant knows from past experience that the amount of time that it takes to write a report for his clients is normally distributed with a mean of 20 hours and a standard deviation of 4 hours. In addition, historically the amount of statistical work done for each report is normally distributed with a mean of 20 hours and a standard deviation of 8 hours. The correlation between report writing time and statistical analysis is 0.8. What is the probability that the total work for the client will be less than 60 hours?

Explanation / Answer

let total work for the client =W=X+Y ; where X is  amount of time that it takes to write a report for his clients and Y  amount of statistical work done

hence total time mean =20+20=40

and std deviation of total time =(42+82+2*0.8*(4*8))1/2 =11.45

P(W<60)=P(Z<(60-40)/11.45)=P(Z<1.7461)=0.9596

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