Suppose x has a distribution with μ = 12 and σ = 4. (a) If a random sample of size n = 41 is drawn, find μx, σ x and P(12 ≤ x ≤ 14). (Round σx to two decimal places and the probability to four decimal places.) μx = σ x = P(12 ≤ x ≤ 14) = (b) If a random sample of size n = 73 is drawn, find μx, σ x and P(12 ≤ x ≤ 14). (Round σ x to two decimal places and the probability to four decimal places.) μx = σ x = P(12 ≤ x ≤ 14) = (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is ---Select--- smaller than the same as larger than part (a) because of the ---Select--- larger smaller same sample size. Therefore, the distribution about μx is ---Select--- the same wider narrower .
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!
Suppose x has a distribution with μ = 12 and σ = 4.
(a) If a random sample of size n = 41 is drawn, find μx, σ x and P(12 ≤ x ≤ 14). (Round σx to two decimal places and the probability to four decimal places.)
| μx = |
| σ x = |
| P(12 ≤ x ≤ 14) = |
(b) If a random sample of size n = 73 is drawn, find μx, σ x and P(12 ≤ x ≤ 14). (Round σ x to two decimal places and the probability to four decimal places.)
| μx = |
| σ x = |
| P(12 ≤ x ≤ 14) = |
(c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)
The standard deviation of part (b) is ---Select--- smaller than the same as larger than part (a) because of the ---Select--- larger smaller same sample size. Therefore, the distribution about μx is ---Select--- the same wider narrower .
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