Question

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 1

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,

$z=\frac{x-\mu}{\sigma}$

Where, $\mu$ is mean,

$\sigma$ is standard deviation,

Given,

For method A,

$\mu = 33$

$\sigma=8$

Thus, the z score for 34 is,

$z_1=\frac{34-33}{8}=0.125$

While, for method B,

$\mu = 37$

$\sigma = 4$

Thus, the z score for 34 is,

$z_2=\frac{34-37}{4}=-0.75$,

Since, $z_1 > z_2$

Hence, method A is preferred if the procedure must be completed within 34 minutes.