Assume that the variable is normally distributed, the average time it takes a group of senior high school students to complete a certain examination is 46.2 minutes while the standard deviation is 8 minutes. What is the probability that a randomly selected senior high school students will complete the examination in less than 43 minutes? Does it seem reasonable that a senior high school student would finish the examination in less than 43 minutes? If 50 randomly selected senior high school students take the examination, what is the probability that the mean time it takes the group to complete the test will be less than 43 minutes? Does it seem reasonable that the mean of the 50 senior high school students could be less than 43 minutes?
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!
Assume that the variable is
- If 50 randomly selected senior high school students take the examination, what is the probability that the mean time it takes the group to complete the test will be less than 43 minutes?
- Does it seem reasonable that the mean of the 50 senior high school students could be less than 43 minutes?
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