Question

Hospital records show that a certain surgical procedure takes on an average 111.6 minutes with a standard deviation of 2.8 minutes. At least what percentage of these surgical procedures take anywhere between 97.6 and 125.6 minutes?

Answer 1

Answer:

At least 37.74% of the procedures takes between 97.6 and 125.6 minutes

Step-by-step explanation:

The percentage is the area of the standard normal distribution curve between the values 97.6 and 125.6

The standard normal variate of the given data is found as

$Z=\frac{X-\overline{X}}{\sigma }$

Thus for the given values Z is calculated as under

$Z_1=\frac{97.6-111.6}{2.8}=-5$

Similarly for the other value we have

$Z_2=\frac{125.6-111.6}{2.8}=5$

Thus the area between the calculated values can be found from standard normal distribution table to be 37.74%