The amount of syrup that people put on their pancakes is normally distributed with mean 55 mL and standard deviation 7 mL. Suppose that 15 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible. b. What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N(?) (?) c.If a single randomly selected individual is observed, find the probability that this person consumes is between 54.4 mL and 56.5 mL. ? d. For the group of 15 pancake eaters, find the probability that the average amount of syrup is between 54.4 mL and 56.5 mL?
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!
The amount of syrup that people put on their pancakes is
b. What is the distribution of
¯
x
x¯
?
¯
x
x¯
~ N(?) (?)
c.If a single randomly selected individual is observed, find the
d. For the group of 15 pancake eaters, find the probability that the average amount of syrup is between 54.4 mL and 56.5 mL?
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