n a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.4. Answer parts (a)-(d) below. (a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 490. The probability that a randomly selected medical student who took the test had a total score that was less than 490 is _____ (Round to four decimal places as needed.) (b) Find the probability that a randomly selected medical student who took the test had a total score that was between 498 and 510. The probability that a randomly selected medical student who took the test had a total score that was between 498 and 510 is _____ .(Round to four decimal places as needed.) (c) Find the probability that a randomly selected medical student who took the test had a total score that was more than 526. The probability that a randomly selected medical student who took the test had a total score that was more than 526 is_____. (Round to four decimal places as needed.)
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 total scores for a certain standardized test were
Answer parts (a)-(d) below.
(a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 490.
Z =
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