A population of values has a distribution with μ=15.3band σ=92.6 You intend to draw a random sample of size n=65 According to the Central Limit Theorem: (a) What is the mean of the distribution of sample means? μ¯x=? (b) What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) σ¯x=? (c) In a random sample of n=65, what is the probability that its random sample mean is more than 23.4? Round to three decimal places. (d) In a random sample of n=65, what is the probability that its random sample mean is less than 4? Give your answer to three decimal places.

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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!