Question

The duration of routine operations in a certain hospital has approximately a normal distribution with an

Answer 1

Answer:  The percentage of operations last longer  than 138 minutes =15.87%

Step-by-step explanation:

Let x denotes the duration of routine operations in a certain hospital.

Given: The duration of routine operations has approximately a normal distribution with $\mu$ = 120 minutes and $\sigma=$ 18 minutes.

The probability that operations last longer  than 138 minutes = $P(X>138)$

$=P(\dfrac{X-\mu}{\sigma}>\dfrac{138-120}{18})\\\\=P(Z>1)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z$

The percentage of operations last longer  than 138 minutes =15.87%