A pizza company advertises that it puts 0.5 pounds of real mozzarella cheese on its medium pizzas. Suppose that the amount of cheese on a randomly selected medium pizza is normally distributed with a mean value of 0.5 pounds and a standard deviation of 0.005 pounds. (Let y = the amount of cheese on a medium pizza. Round the answers to three decimal places.) (a) What is the probability that the amount of cheese on a medium pizza is between 0.505 and 0.510 pounds? P(0.505 ≤ y ≤ 0.510) = (b) What is the probability that the amount of cheese on a medium pizza exceeds the mean value by more than 2 standard deviations? P(y > ? + 2?) = (c) What is the probability that four randomly selected medium pizzas all have at least 0.495 pounds of cheese?
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!
A pizza company advertises that it puts 0.5 pounds of real mozzarella cheese on its medium pizzas. Suppose that the amount of cheese on a randomly selected medium pizza is
P(0.505 ≤ y ≤ 0.510) =
(b) What is the probability that the amount of cheese on a medium pizza exceeds the mean value by more than 2 standard deviations?
P(y > ? + 2?) =
(c) What is the probability that four randomly selected medium pizzas all have at least 0.495 pounds of cheese?
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