Question

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take more than four hours to construct a soapbox derby car.

Answer 1

The probability that it would take more than four hours to construct a soapbox derby car = 0.1587 or 15.87
`\%`

Explanation:

Given -

Mean
`(\\u )` = 3 hours

Standard deviation
`(\sigma )` = 1 hours

Let X be the no of hours to construct a soapbox derby car

the probability that it would take more than four hours to construct a soapbox derby car =

`P(X > 4)` =
`P((X - \\u )/(\sigma)> (4 - 3 )/(1))`

=
`P(Z > 1)` Put
`(Z = (X - \\u )/(\sigma))`

= 1 -
`P(Z < 1)`

= 1 - .8413 Using z table

= 0.1587