Question

A machine fills medication bottles. Even though the bottles are labeled “32 fl.oz.,” because the machine is not exact, the manufacturer sets the machine at 34 fl.oz, hoping to avoid underfilling the bottles. The actual amount of medication filled by the machine is approximately normal with mean of 34 fl.oz. and standard deviation of 1.8 fl.oz.

1. (4 pts) What is the probability a randomly chosen bottle has less than 32 fl.oz. of medication?

2. (6 pts) The state consumer protection agency understands that some bottles will be underfilled so they won’t penalize the company if a random bottle here and there goes under 32 fl.oz. But they will penalize the company if they take a random sample of 50 bottles and the 50 bottles have a mean below 32 fl.oz. What is the probability the company gets penalized? Show your work completely including checking conditions. (If the conditions are not met, say so but proceed anyway.)

Answer 1

Ans. Since the machine follows Aprroximately Normal Distribution, We can assume X ~ N(34,1.8^2) to find the values of the probabilities.