The Absent-Minded Bakery sells both cream-filled and jelly-filled donuts. In the morning rush, the bakers forgot which batch was cooling on which tray and now need help in identifying the two trays. The weights of jelly-filled donuts follow a uniform distribution from 37 to 45 g. The mean weight of jelly-filled donuts is 41 g with a standard deviation of 2.31 g. The weights of cream-filled donuts follow a normal distribution with a mean of 37.5 g and a standard deviation of 1.5 g. The bakery will set their two hypotheses as follows: H_0H 0 : The tray contains jelly-filled donuts H_aH a : The tray contains cream-filled donuts. We randomly select and weigh a donut from the tray. If the donut weighs 39 g or less, we'll decide that the tray it came from contains cream-filled donuts; that is we will reject H_0H 0 .

A baker who is particularly well-versed in statistics remembers that the results of hypothesis tests are more accurate if a larger sample is taken. The baker decides to repeat the test, but this time weighing the entire tray of 36 donuts and calculating the average donut weight to make the decision. The baker updates the decision rule to reject H_0

H0

if the average donut weight for the tray is 39 g or less.

What distribution will we use to calculate the significance level of this new test?

Uniform (37, 45)

Normal (37.5, 1.5)

Normal (41, 0.385)

Normal (41, 2.31)

Normal (37.5, 0.25)