Spring 2017 I. A machine that produces ball bearings has initially been set soth

Question

Spring 2017 I. A machine that produces ball bearings has initially been set sothatthe true average diameter of the bearings it produces is 500 in. A bearing is acceptable within this target value. Suppose, however, that the setting changed during the course of so the bearings have normally distributed diameters with mean value A99 in. and standard deviation .002 in. What percentage of the bearings produced will not be acceptable? 2. Let z be a standard normal random variable. (a) Find the following probability. (i) P(Z 0.61) (b) Find the value of the constant c that makes the probability statement correct. (ii) P(Z c) 0.3336 (iv) Poszsc) 0.3186

Explanation / Answer

1) Mean = 0.499 in

Standard deviation = 0.002 in

Acceptable range = 0.496 to 0.504

Probability of a non acceptable bearing =P(X < 0.496) and P(X > 5.004)

P(X < 0.496) = P(Z < (0.496 - mean)/standard deviation)

= P(Z < (0.496 - 0.499)/0.002)

= P(Z < -1.5)

= 0.0668

P(Z > 0.504) = 1 - P(Z < 0.504)

= 1 - P(Z < (0.504 - 0.499)/0.002)

= 1 - P(Z < 2.5)

= 1 - 0.9938

= 0.0062

Percentage of non acceptable bearing = 0.0668+0.0062 = 0.073 = 7.3%

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