Suppose p=0.875 is the proportion of Canadians who are willing to get vaccinated against COVID-19. We ask a sample of n= 400 canadians if they are willing to get vaccinated against COVID-19. Let X equal the number of individuals in the sample who say "yes". (Since 400 is much less than 5% of the total population of 37 million, we can assume that each response is independent, which makes X a binomial random variable.) Which Excel command gives the probability that at least 380 Canadians in the sample say "yes"? = 1-BINOM.DIST(379, 400, 0.875, TRUE) = 1-BINOM.DIST(380, 400, 0.875, TRUE) = BINOM.DIST(379, 400, 0.875, TRUE) = BINOM.DIST(380, 400, 0.875, TRUE)
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!
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