After the recent movie Abominable, Yeti farms have become all the rage internationally. The League of Yeti Farmers (LYF) have had to clamp down on breeding practices because of a dangerous drug that that increases the number of offspring a Yeti female can have in a given year. Yeti are notoriously slow to reproduce, with an average of 3 offspring per decade with a standard deviation of 1.5. Assume the distribution of offspring per decade is normal. Include all work in the upload file. A. What is the probability that a randomly selected Yeti female produced at least four offspring in the last decade? (Round to four decimal places) ?(?≥4) B. If a LYF inspector discovered such a Yeti female, would that cause them to be concerned that this Yeti is being given the drug? This (is or is not) unusual, % of Yeti females will have at least 4 offspring in a decade. C. Let us instead look at a herd of 10 Yeti females and the total number of offspring they have in a decade. What can we say about the probability distribution of sample sums, ∑?∑x, of simple random samples of size ten Yeti females? What would the mean and standard deviation of this distribution be? State the theorem used to support your answer. (Round the standard deviation to three 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!
After the recent movie Abominable, Yeti farms have become all the rage internationally. The League of Yeti Farmers (LYF) have had to clamp down on breeding practices because of a dangerous drug that that increases the number of offspring a Yeti female can have in a given year. Yeti are notoriously slow to reproduce, with an average of 3 offspring per decade with a standard deviation of 1.5. Assume the distribution of offspring per decade is normal.
Include all work in the upload file.
A. What is the
?(?≥4)
B. If a LYF inspector discovered such a Yeti female, would that cause them to be concerned that this Yeti is being given the drug?
This (is or is not) unusual, % of Yeti females will have at least 4 offspring in a decade.
C. Let us instead look at a herd of 10 Yeti females and the total number of offspring they have in a decade. What can we say about the probability distribution of sample sums, ∑?∑x, of simple random samples of size ten Yeti females? What would the mean and standard deviation of this distribution be? State the theorem used to support your answer. (Round the standard deviation to three decimal places.)
The Distribution of ∑?∑x is , with a mean of and standard deviation of .
D. What is the probability that a randomly selected sample of ten Yeti females produced at least of 40 offspring (That's about 4 each) in the last decade? (Round to four decimal places)
?(∑?≥40)
E. If a LYF inspector discovered that a Yeti farm has 10 Yeti females with this total, would that cause them to be concerned that the Yetis on this farm are being given the drug?
This (is or is not) unusual, % of herds of 10 Yeti females will have at least 40 offspring in a decade.
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