Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 33 minutes and a standard deviation of 8 minutes, while method B has a mean of 37 minutes and a standard deviation of 4.0 minutes. (a) Which procedure is preferred if the procedure must be completed within 34 minutes?

Answer:Method A.Step-by-step explanation:For solving this question we need to find out the z-scores for both methods,Since, the z-score formula is,[tex]z=\frac{x-\mu}{\sigma}[/tex]Where, [tex]\mu[/tex] is mean,[tex]\sigma[/tex] is standard deviation,Given,For method A,[tex]\mu = 33[/tex][tex]\sigma=8[/tex]Thus, the z score for 34 is,[tex]z_1=\frac{34-33}{8}=0.125[/tex]While, for method B,[tex]\mu = 37[/tex][tex]\sigma = 4[/tex]Thus, the z score for 34 is,[tex]z_2=\frac{34-37}{4}=-0.75[/tex],Since, [tex]z_1 > z_2[/tex]Hence, method A is preferred if the procedure must be completed within 34 minutes.