Question

The local bakery bakes more than a thousand standard loaves of bread daily, and the weights...

The local bakery bakes more than a thousand standard loaves of bread daily, and the weights of these loaves follow a normal distribution. The long term mean weight is 482 grams and the standard deviation of the weights is 18 grams.
a) An individual loaf is measured and weighs 478 grams. What is the probability that an individual loaf will weigh less than 478grams.
b) What is the sampling distribution of the mean weight of loaves if samples of size 36 were taken from the population?
c) Sketch both the population and the sampling distribution on the same axis, including the mean and approximate range of both distributions. Ensure correct labelling.
d) What is the probability that a sample mean (from n = 36) will have a value less than 478 grams?
e) If the sample size was changed to 144, state how the sampling distribution would change in position and shape.
f) Would these calculations above be valid if the population distribution was skewed? EXPLAIN clearly, stating the concept or theory that is involved in this situation

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