Question

4. The time needed to complete the final exam in statistics at CAU is normally distributed with a mean of 90 minutes and a standard deviation of 10 minutes.What is the probability that the exam will be completed in one hour or less

Answer 1

The value is
`P(X \le 60 ) = 0.00135`

Explanation:

From the question we are told that

The mean is
`\mu = 90 \ minutes`

The standard deviation is
`\sigma = 10`

Generally 1 hours = 60 minutes

Generally the probability that the exam will be completed in one hour or less is

`P(X \le 60 ) = 1 - P(X > 60 )`

Here

`P(X > 60 ) = P( ( X - \mu )/( \sigma ) > ( 60 - 90 )/( 10 ) )`

`(X -\mu)/(\sigma )  =  Z (The  \ standardized \  value\  of  \ X )`

`P(X > 60 ) = P( Z> -3 )`

From the z -distribution table the probability of ( Z> -3 )

`P( Z> -3 ) = 0.99865`

`P(X > 60 ) = 0.99865`

=>
`P(X \le 60 ) = 1 - 0.99865`

=>
`P(X \le 60 ) = 0.00135`