In a population of Siberian flying squirrels in western Finland, assume that the the number of pups born to each female over her lifetime has mean ?=3.66μ=3.66 and standard deviation ?=2.9598.σ=2.9598. The distribution of squirrel pups born is non‑normal because it takes only whole, non‑negative values. Determine the mean number of pups, ?⎯⎯⎯,x¯, such that in 70%70% of all random samples of such squirrels of size ?=40,n=40, the mean number of pups born to females in the sample is less than ?⎯⎯⎯.than x¯. You may need to use software or a table of ?-z-critical values. You may find some software manuals useful. Give your answer to at least two decimal places. ?⎯⎯⎯= ?
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!
In a population of Siberian flying squirrels in western Finland, assume that the the number of pups born to each female over her lifetime has
Determine the mean number of pups, ?⎯⎯⎯,x¯, such that in 70%70% of all random samples of such squirrels of size ?=40,n=40, the mean number of pups born to females in the sample is less than ?⎯⎯⎯.than x¯.
You may need to use software or a table of ?-z-critical values. You may find some software manuals useful.
Give your answer to at least two decimal places.
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