II. 1. A t-distribution is composed of bell-shaped curves. Each curve represents a degree of freedom. Tell whether the statement is TRUE or FALSE. 2. The t-distribution is not symmetric to its mean. It means that the distribution at the left of the mean is not the same as the distribution at the right of the mean. 3. The variance of the distribution is greater than one unit. 4. As the sample size decreases, the t-distribution approaches the standard normal distribution. 5. The total area under any of the curves is equal to 1.
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!
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