# Production under normally distributed process

A production process manufactures items with weights that are normally distributed with

mean 16 pounds and standard deviation 0.15 pound. An item is considered to be defective if its weight is less than 15.8 pounds or greater than 16.2 pounds. Suppose that these items are currently produced in batches of 200 units. [Hint: First, use the normal distribution to find the probability of obtaining a non-defective item, then use an appropriate binomial distribution to answer parts (a) and (b).]

(a) Find the probability that at most 17.5% of the items in a given batch will be defective.

(b) Find the probability that at least 75% of the items in a given batch will be acceptable.

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#### Solution Preview

mean (mu) = 16 pound

SD = 0.15

Defective, if wt (X) is less than 15.8(x1) or greater than 16.2 (x2) pounds respectively.

Probability of defective p = P( 15.8 > X > 16.2)

z1 = (x1 - mu)/SD = (15.8 - 16)/0.15 = -1.33

z2 = (x2 - ...

#### Solution Summary

A problem solved related normally distributed production process, where probability of defective items is estimated.