box contains the 50 numbers, of which 18 are negative (less than zero), 12 between 0 and 10, with the remaining 20 being bigger than 10. We will make 25 draws from this box, one at a time, with replacement. Let the random variable X be the COUNT of negative numbers among the 25 sampled. Let Y be the COUNT of numbers bigger than 10 among the 25 sampled. The random variable Y has a binomial distribution with n=25 and p=0.40. Also use the binomial excel spreadsheet to help you find P(Y<9). ["", "", "", "", ""] Note: this asks for < where the spreadsheet gives ≤ What is the mean of Y? ["", "", "", ""] What is the standard deviation of Y?
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!
A box contains the 50 numbers, of which 18 are negative (less than zero), 12 between 0 and 10, with the remaining 20 being bigger than 10. We will make 25 draws from this box, one at a time, with replacement. Let the random variable X be the COUNT of negative numbers among the 25 sampled. Let Y be the COUNT of numbers bigger than 10 among the 25 sampled.
The random variable Y has a binomial distribution with n=25 and p=0.40.
Also use the binomial excel spreadsheet to help you find P(Y<9). ["", "", "", "", ""]
Note: this asks for < where the spreadsheet gives ≤
What is the mean of Y? ["", "", "", ""]
What is the standard deviation of Y?
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