Question

Weights of cereal in 16 ounce boxes are normally distributed with a mean of 16 ounces and a standard

deviation of 0.12 ounce. Respond to the following:

a)What is the probability that a cereal box selected at random will have at least 15.95 ounces?

b)What is the probability that the mean of a sample of 16 boxes will be at least 15.95 ounces?

c)In a production of 10,000 boxes, how many would you expect to be below 15.95 ounces?

d)The production manager was concerned that his boxes of cereal had significantly lower weight than the expected value of 16 ounces. A sample of 50 boxes was obtained and the mean weight found to be 15.95 ounces with a standard deviation of 0.12 ounces. Evaluate this situation using appropriate hypothesis testing.

Answer 1

a)  The probability that a cereal box selected at random will have at least 15.95 ounces is

b)  The probability that the mean of a sample of 16 boxes will be at least 15.95 ounces is

c) In a production of 10,000 boxes, The number of boxes at least 15.95 ounces is 10000*0.66154 = 6615

The number of boxes below 15.95 ounces is 10,000 - 6,615 = 3385

d)

H0: The production manager was concerned that his boxes of cereal had not significantly lower weight than the expected value of 16 ounces

H1: The production manager was concerned that his boxes of cereal had significantly lower weight than the expected value of 16 ounces

i.e.

Thus we conclude that The production manager was concerned that his boxes of cereal had significantly lower weight than the expected value of 16 ounces