What distribution will we use to calculate the significance level of this new test? O Uniform (37, 45) Normal (37.5, 1.5) Normal (41, O.385) O Normal (41, 2.31) O Normal (37.5, 0.25)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Distribution needed to calculate significance level
![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 mea
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:
Ho: The tray contains jelly-filled donuts
Ha: 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 Ho.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf2bf022-7285-41ce-8dd3-ba3b182bde05%2Fcd84f343-bc5c-4798-b22a-7fa458bccdba%2Fcfmjgo8_processed.png&w=3840&q=75)
![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 Ho 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)
O Normal (37.5, 1.5)
Normal (41, O.385)
Normal (41, 2.31)
O Normal (37.5, 0.25)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf2bf022-7285-41ce-8dd3-ba3b182bde05%2Fcd84f343-bc5c-4798-b22a-7fa458bccdba%2F5oplqft_processed.png&w=3840&q=75)
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