Question

A manufacturing process produces flat washers with an intended diameter of 12mm. In fact, the population diameter has a mean of μ=12.3mm and standard deviation of σ=.5mm. Tomorrow 1,000 washers will be produced and shipped. The diameter of the washers is known to be approximately normal. How many washers in the shipment can be expected to have a diameter between 12mm and 13mm?

Answer 1

Given,

= 12.3 , = 0.5

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

So,

P(12 < X < 13) = P(X < 13) - P(X < 12)

= P(Z < (13- 12.3) / 0.5) - P(Z < (12 - 12.3) / 0.5)

= P(Z < 1.4) - P(Z < -0.6)

= 0.9192 - 0.2743

= 0.6449

Of the 1000 washers , we expect = 0.6449 * 1000 = 645