Can researchers carry out their analysis assuming an approximation to the normal distribution is acceptable? B) Calculate the probability of observing the results witnessed in the sample. C) Determine the mean and standard deviation for this distribution under the assumptions made in part A.
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!
Researchers are concerned about the binge drinking behaviors at a local university among members of Greek life organizations. Assume the college reported that binge drinking was observed in 31% of students attending the university. The research team conducts a sample of 213 students involved in a Greek life organization on campus, and finds that 94 have reported binge drinking behaviors at least once that year.
A) Can researchers carry out their analysis assuming an approximation to the
B) Calculate the probability of observing the results witnessed in the sample.
C) Determine the mean and standard deviation for this distribution under the assumptions made in part A.
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