Keith is a drummer who purchases his drumsticks online. When practicing with the newest pair, he notices they feel heavier than usual. When he weighs one of the sticks, he finds that it is 2.23 oz. The manufacturer's website states that the average weight of each stick is 1.85 oz with a standard deviation of 0.18 oz. Assume that the weight of the drumsticks is normally distributed. What is the probability of the stick's weight being 2.23 oz or greater? Give your answer as a percentage precise to at least two decimal places. You might find this table of standard normal critical values useful.
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!
Keith is a drummer who purchases his drumsticks online. When practicing with the newest pair, he notices they feel heavier than usual. When he weighs one of the sticks, he finds that it is 2.23 oz. The manufacturer's website states that the average weight of each stick is 1.85 oz with a standard deviation of 0.18 oz. Assume that the weight of the drumsticks is
What is the probability of the stick's weight being 2.23 oz or greater? Give your answer as a percentage precise to at least two decimal places.
You might find this table of standard normal critical values useful.
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