In a recent year, the MCAT total scores were normally distributed, with a mean of 500 and a standard deviation of 10.6. In what range would you expect to find the middle 98% of scores? Write your answers in interval notation, rounded to the nearest tenth. If you were to draw samples of size 60 from this population, in what range would you expect to find the middle 98% of most averages for the scores in this sample? Use the Central Limit Theorem, write your answer in interval notation, rounding to the nearest tenth. Find the probability that a randomly selected medical student who took the MCAT has a total score that is more than 522. Round your answer to the nearest thousandth
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!
In a recent year, the MCAT total scores were
In what
If you were to draw samples of size 60 from this population, in what range would you expect to find the middle 98% of most averages for the scores in this sample? Use the Central Limit Theorem, write your answer in interval notation, rounding to the nearest tenth.
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Determine if this
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