Quarters Assume that weights of quarters minted after 1964 are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g (based on U.S. Mint specifications). a. Find the probability that a randomly selected quarter weighs between 5.600 g and 5.700 g. b. If 25 quarters are randomly selected, find the probability that their mean weight is greater than 5.675 g. c. Find the probability that when eight quarters are randomly selected, they all weigh less than 5.670 g. d. If a vending machine is designed to accept quarters with weights above the 10th percentile P10, find the weight separating acceptable quarters from those that are not acceptable.
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!
Quarters Assume that weights of quarters minted after 1964 are
a. Find the
b. If 25 quarters are randomly selected, find the probability that their mean weight is greater than 5.675 g.
c. Find the probability that when eight quarters are randomly selected, they all weigh less than 5.670 g.
d. If a vending machine is designed to accept quarters with weights above the 10th percentile P10, find the weight separating acceptable quarters from those that are not acceptable.
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