A random sample of 10 stock market mutual funds was taken. Suppose that rates of returns on the population of all stock market mutual funds follow a normal distribution.a. The probability is 0.10 that sample variance is greater than what percentage of the population variance?b. Find any pair of numbers, a and b, to complete the following sentence: The probability is 0.95 that the sample variance is between a% and b% of the population variance.c. Suppose that a sample of 20 mutual funds had been taken. Without doing the calculations, indicate how this would change your answer to part (b).
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 random sample of 10 stock market mutual funds was taken. Suppose that rates of returns on the population of all stock market mutual funds follow a normal distribution.
a. The probability is 0.10 that sample variance is greater than what percentage of the population variance?
b. Find any pair of numbers, a and b, to complete the following sentence: The probability is 0.95 that the sample variance is between a% and b% of the population variance.
c. Suppose that a sample of 20 mutual funds had been taken. Without doing the calculations, indicate how this would change your answer to part (b).
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