what percent of the area under the normal distribution falls bewteen 115 and 130? The Standard deviation is 16 and the mean is 100.
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!
what percent of the area under the
I know that I do (115-100)/16 and (130-100)/16 to get the z-scores 0.94 and 1.89. The percentages I get are 32.64 and 47.06.
My question is, what do I do with those percentages now? Do I subtract 47.06% from 32.64%?
Given information-
Population mean, μ = 100
Population standard deviation, σ = 16
Thus, X ~ N (100, 16)
We have to find the percentage of the area under normal distribution falls between 115 and 130.
P (115<X<130) = P (X<130) - P (X<115)
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