Question

The pressure of a pressure washer is normally distributed with a mean of 2510 psi and a standard deviation of 90 psi.

a) If all washers with pressure less than 2400 or greater than 2600 psi are considered defective, find the probability that a randomly selected washer is defective.

b) Determine the value of x, so that 99% of all washers have pressure within 2510 +/- x psi.

Answer 1

Let ,

a) Now ,

; From standard normal probability table

Therefore , the probability that a randomly selected wsher is defective is 0.2699

b) Now ,

............(I)

Also , From standard normal probability table, ............(II)

From (I) and (II) , we get ,

Therefore , the x=2277.80 , so that 99% of all washers have pressure within 2510 psi.