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

Answer:

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

Step-by-step explanation:

Given -

Mean $(\nu )$  = 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 =

$P(X > 4)$  = $P(\frac{X - \nu }{\sigma}> \frac{4 - 3 }{1})$

                = $P(Z > 1)$                   Put $(Z = \frac{X - \nu }{\sigma})$

                 =  1 -  $P(Z < 1)$            

                 =  1 - .8413                    Using z table

                  = 0.1587