Answer to Question #251292 in Statistics and Probability for orange

Question

A machine produces vitamin C tablets, the diameters of which are normally distributed with mean 10mm and a standard deviation of 0.1mm. A tablet is acceptable if its diameter lies between 9.81mm and 10.19mm. To pass a quality test, at least 90% of the tablets in a pack should be acceptable.

(a) Determine the probability that a tablet is acceptable. [5 marks]

(b) What is the probability that a pack of 20 tablets will pass the quality test? Use binomial probability distribution.

(c) What is the probability that a pack of 200 tablets will pass the quality test?

(d) If you have a choice of submitting a pack of 20 tablets or a pack of 200 tablets for the quality test, which one would you prefer and why?