1. A candle maker produces jar candles that have a label weight of 20.4 oz. Assume that the distribution of the weights of these candles is N (21.37,0.16). Let X denote the weight of a candle selected at random from the production line.

1. (a)  Let X bar equal the sample mean of the 100 candles selected randomly. Find P (21.31 ≤ Xbar ≤ 21.39).
2. (b)  Determine the minimum weight of the heaviest 2.5% of all candles. In other words, what is c satisfying P (X >c) = 0.025?
3. (c)  Suppose that 15 candles are randomly selected and weighted. Let Y equal the number of these candles that weight less than 20.857 oz. Find P (Y ≤ 2).
4. (d)  Now suppose 100 candles are randomly selected. Let W equal the number of these candles that weight less than 20.857 oz. Using the CLT (Central Limit Theorem), approximate P(W ≤ 5).