Which of the following correctly compares the tt-distribution and zz-distribution? A. For small sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric. B. For large sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric. C. The curves of both distributions are symmetric, but the height of the density curve of the t-distribution is taller than the height of the density curve of the z-distribution. D. The area under the density curve of the t-distribution is greater than the area under the density curve of the z-distribution, especially for small sample sizes. E. The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample size
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!
Which of the following correctly compares the tt-distribution and zz-distribution?
A. For small
B. For large sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric.
C. The curves of both distributions are symmetric, but the height of the density curve of the t-distribution is taller than the height of the density curve of the z-distribution.
D. The area under the density curve of the t-distribution is greater than the area under the density curve of the z-distribution, especially for small sample sizes.
E. The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes.
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