Question

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 11 ounces. a. The process standard deviation is .20 ounces, and the process control is set at plus or minus standard deviations. Units with weights less than or greater than ounces will be classified as defects. What is the probability of a defect (to 4 decimals)

Answer 1

The question supplied is incomplete :

The x parameters aren't given ; "Units with weights less than or greater than ounces will be classified as defects"

Assume the unit weights Given are ;

Units with weights less than 10.8 or greater than 11.2 ounces will be classified as defects

Just follow the procedure in the solution for any value of unit weight interval given.

Answer:

0.3173

Explanation:

Mean weight, m = 11 ounces

Standard deviation, s = 0.2 ounces

Find the Zscore for each unit weight :

Z = (x - mean) / standard deviation

P(x < 10.8) :

Z = (10.8 - 11) / 0.2 = - 1

P(Z < - 1) = 0.15866

P(x > 11.2) :

Z = (11.2 - 11) / 0.2 = 1

P(Z > 1) = 0.84134

P(x < 11.2) - P(x < 10.8) = 1 - (P(Z < 1) - P(Z < - 1)) = 1 - 1 - (0.84134 - 0.15866) = 1 - 0.68268 = 0.31732

Hence, Probability of a defect is 0.3173