Question

3. The packaging process in a breakfast cereal company has been adjusted so that an average of μ = 13.0 oz of cereal is placed in each package. The standard deviation of the actual net weight is σ = 0.1 oz and the distribution of weights is known to followthe normal probability distribution.
a. what is the population mean weight of the packaging process?

b. what is the population standard deviation of the packaging process?

c. what proportion of cereal packages X contain less than 12.9 oz? (in decimal format, round to 4 decimal digits, e.g. 0.1111)

d.Suppose 25 cereal boxes are chosen at random, what is the mean weight of all possible sample means μ(x_bar)?

e. Suppose 25 cereal boxes are chosen at random,  what is the standard deviation of all possible sample means  (standard error)? (round to 2 decimal digits, e.g. 0.11)

f. Suppose 25 cereal boxes are chosen at random, what proportion of sample means X_bar will be less than 12.9 oz? (in decimal format, round to 4 decimal digits, e.g. 0.1111)

Answer 1