A population is normally distributed with mean 15.9 and standard deviation 1.1. (a) Find the intervals representing one, two, and three standard deviations of the mean. one standard deviation (smaller value) (larger value) two standard deviations (smaller value) (larger value) three standard deviations (smaller value) (larger value) (b) What percent of the data lies in each of the intervals in part (a)? (Round your answers to two decimal places.) one standard deviation % two standard deviations % three standard deviations % (c) Draw a sketch of the bell curve.
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!
A population is
| one standard deviation | (smaller value) |
| (larger value) | |
| two standard deviations | (smaller value) |
| (larger value) | |
| three standard deviations | (smaller value) |
| (larger value) |
(b) What percent of the data lies in each of the intervals in part (a)? (Round your answers to two decimal places.)
| one standard deviation | % |
| two standard deviations | % |
| three standard deviations | % |
(c) Draw a sketch of the bell curve.
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