Rainfall Statistics from Cornell’s Northeast RegionalClimate Center indicate that Ithaca, NY, gets an averageof 35.4′′ of rain each year, with a standard deviation of4.2′′. Assume that a Normal model applies.a) During what percentage of years does Ithaca get morethan 40′′ of rain?b) Less than how much rain falls in the driest 20% of allyears?c) A Cornell University student is in Ithaca for 4 years.Let y represent the mean amount of rain for those4 years. Describe the sampling distribution model ofthis sample mean, y.d) What’s the probability that those 4 years average lessthan 30′′ of rain?
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!
Rainfall Statistics from Cornell’s Northeast Regional
Climate Center indicate that Ithaca, NY, gets an average
of 35.4′′ of rain each year, with a standard deviation of
4.2′′. Assume that a Normal model applies.
a) During what percentage of years does Ithaca get more
than 40′′ of rain?
b) Less than how much rain falls in the driest 20% of all
years?
c) A Cornell University student is in Ithaca for 4 years.
Let y represent the mean amount of rain for those4 years. Describe the sampling distribution model of
this sample mean, y.
d) What’s the probability that those 4 years average less
than 30′′ of rain?
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