The true weight of "10-pound" sacks of potatoes processed at a certain packaging house follows a normal distribution with mean of 10.1 pounds and standard deviation of 0.2 pounds.
a) What is the probability that a sack weighs at least 10 pounds?
b) A random sample of 9 sacks is selected. What is the probability that the average weight of these 9 is at least 10 pounds?
c) Use a computer for this part. Generate S = 1000 random samples from a normal distribution with mean of 10.1 and standard deviation of 0.2. Use sample size n = 9.
For each of the s = 1 : 1000 datasets, compute the sample mean x .
Make a histogram for the 1000 values of x .
What is the proportion of values of x ( among the 1000 values of x generated ) that are at least 10 pounds?