Question

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

average of 120 minutes and a standard deviation of 18 minutes. What percentage of operations last longer
than 138 minutes?

Answer 1

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

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((X-\mu)/(\sigma)>(138-120)/(18))\\\\=P(Z>1)\ \ \ [Z=(X-\mu)/(\sigma)]\\\\=1-P(Z<1)\\\\=1- 0.8413\\\\=0.1587`

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