Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 4​%. A​ mutual-fund rating agency randomly selects 27 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 3.48​%. Is there sufficient evidence to conclude that the fund has moderate risk at the α=0.01 level of​ significance? A normal probability plot indicates that the monthly rates of return are normally distributed. What are the correct hypotheses for this​ test?   The null hypothesis is H0​: ▼   muμ sigmaσ pp ▼   equals= not equals≠ less than< greater than> ▼   0.0348. 0.04. The alternative hypothesis is H1​: ▼   sigmaσ pp muμ ▼   greater than> not equals≠ less than< equals= ▼

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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!