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 [tex]\mu[/tex] = 120 minutes and [tex]\sigma=[/tex] 18 minutes.
The probability that operations last longer than 138 minutes = [tex]P(X>138)[/tex]
[tex]=P(\dfrac{X-\mu}{\sigma}>\dfrac{138-120}{18})\\\\=P(Z>1)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<1)\\\\=1- 0.8413\\\\=0.1587[/tex]
The percentage of operations last longer than 138 minutes =15.87%
