# Question

The data below are the net weights (in grams) for a sample of 30 bags of M&M’s. The advertised net weight is 47.9 grams per bag.

The FDA requires that (nearly) every bag contain the advertised weight; otherwise, violations (less than 47.9 grams per bag) will bring about mandated fines. (M&M’s are manufactured and distributed by Mars Inc.)

a. What percentage of the bags in the sample are in violation?

b. If the weight of all filled bags is normally distributed with a mean weight of 47.9 g, what percentage of the bags will be in violation?

c. Assuming the bag weights are normally distributed with a standard deviation of 1.5 g, what mean value would leave 5% of the weights below 47.9 g?

d. Assuming the bag weights are normally distributed with a standard deviation of 1.0 g, what mean value would leave 5% of the weights below 47.9 g?

e. Assuming the bag weights are normally distributed with a standard deviation of 1.5 g, what mean value would leave 1% of the weights below 47.9 g?

f. Why is it important for Mars to keep the percentage of violations low?

g. It is important for Mars to keep the standard deviation as small as possible so that in turn the mean can be as small as possible to maintain net weight. Explain the relationship between the standard deviation and the mean. Explain why this is important to Mars.

The FDA requires that (nearly) every bag contain the advertised weight; otherwise, violations (less than 47.9 grams per bag) will bring about mandated fines. (M&M’s are manufactured and distributed by Mars Inc.)

a. What percentage of the bags in the sample are in violation?

b. If the weight of all filled bags is normally distributed with a mean weight of 47.9 g, what percentage of the bags will be in violation?

c. Assuming the bag weights are normally distributed with a standard deviation of 1.5 g, what mean value would leave 5% of the weights below 47.9 g?

d. Assuming the bag weights are normally distributed with a standard deviation of 1.0 g, what mean value would leave 5% of the weights below 47.9 g?

e. Assuming the bag weights are normally distributed with a standard deviation of 1.5 g, what mean value would leave 1% of the weights below 47.9 g?

f. Why is it important for Mars to keep the percentage of violations low?

g. It is important for Mars to keep the standard deviation as small as possible so that in turn the mean can be as small as possible to maintain net weight. Explain the relationship between the standard deviation and the mean. Explain why this is important to Mars.

## Answer to relevant Questions

The extraction force required to remove a cork from a bottle of wine has a normal distribution with a mean of 310 Newtons and a standard deviation of 36 Newtons. a. The specs for this variable, given in Applied Example 6.13, ...Using the z(a) notation (identify the value of a used within the parentheses), name each of the standard normal variable z’s shown in the following diagrams We are often interested in finding the value of z that bounds a given area in the left-hand tail of the normal distribution, as shown in the accompanying figure. The notation z(a) represents the value of z such that P(z > ...Find the probability that a piece of data picked at random from a normal population will have a standard score (z) that lies to the left of the following z-values a. z = 2.10 b. z = 1.20 c. z = 3.26 d. z = 0.71 Referring to Example 6.21 (p. 302): a. Calculate P(x < 3|B(25, 3 )). b. How good was the normal approximation? Explain.Post your question

0