Question

You may need to use the appropriate appendix table to answer this question. The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions. (a) What is the probability of completing the exam in one hour or less

Answer 1

The probability of completing the exam in one hour or less is 0.0228.

Explanation:

Given: Mean = 80

Standard deviation = 10

To find: The probability of completing the exam in one hour or less.

We have,
`\mu=80` and
`\sigma=10`.

Now, the z-value is the sample mean decreased by the population mean divided by the standard deviation.

`z=\frac{\bar{x}-\mu}{\sigma}`

⇒
`z=(60-80)/(10)`

⇒
`z=-2`

Now,
`z=\frac{\bar{x}-\mu}{\sigma}`

⇒
`z=(75-80)/(10)`

⇒
`z=-0.5`

Again,
`z=\frac{\bar{x}-\mu}{\sigma}`

⇒
`z=(90-80)/(10)`

⇒
`z=1`

Using appropriate appendix table, we get
`P(z<-2)=0.0228`.