Suppose that the number of Facebook friends users have is normally distributed with a mean of 112 and a standard deviation of about 49. Assume fifteen individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) For the group of 15, find the probability that the average number of friends is less than 111. Find the third quartile for the average number of Facebook friends. Round to 2 decimal places. For part b), is the assumption that the distribution is normal necessary? NoYes
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!
Suppose that the number of Facebook friends users have is
- What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
- For the group of 15, find the
probability that the average number of friends is less than 111. - Find the third
quartile for the average number of Facebook friends. Round to 2 decimal places. - For part b), is the assumption that the distribution is normal necessary? NoYes
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