6.67 A flour manufacturer found that the weightage error of bags labeled 2 kilograms of flour follows a normal distribution with a mean of 10 grams and a standard deviation of 2 grams. A random sample of 5 bags of 2 kilograms flour each was taken.

a. What is the probability that the sample mean weightage error is more than 11.5 grams?

b. The probability is 0.10 that the sample mean weightage error is less than how many grams?

c. The probability is 0.10 that the sample standard deviation of weightage error is more than how many grams?

d. The probability is 0.10 that the sample standard deviation of weightage error is less than how many grams?

e. What is the probability that more than three of these bags of 2 kg flour has weightage error more than 11 grams?