The composite scores of individual students on the ACT college entrance examination in 2019 followed a Normal distribution with a mean of 20.8 and a standard deviation of 5.8. a. What is the probability that a single student is randomly chosen from all those taking the test scores 22 or higher? b. Now take an SRS of 50 students who took the test. What is the probability that the mean score of these students is 22 or higher? c. What is the probability that the mean score of an SRS of 100 students is 22 or higher?
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!
The composite scores of individual students on the ACT college entrance examination in 2019 followed a
a. What is the
b. Now take an SRS of 50 students who took the test. What is the probability that the mean score of these students is 22 or higher?
c. What is the probability that the mean score of an SRS of 100 students is 22 or higher?
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