Suppose 30% of students at a large university take Intro Stats. Randomly sample 100 students from this university ane Does this process describe a binomial random variable? in both entry fields. If it is binomlal, give values for n and p. If it is not binomial, enter n = p =
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!
Conditions for Binomial Random Variable:
The process should satisfy the following conditions for being binomial random variable.
- The number of trails (n) is fixed in advance.
- The probability of success (p) is constant for each trail.
- The outcomes of the variable are independent from trail to trail.
The process mentioned is ‘Suppose 30% of students at a large university take Intro Stats. Randomly sample 100 students from this university and count the number who has taken Intro Stats’.
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