The length of a zebra pregnancy (from conception to birth) varies according to a normal distribution with mean 377 days and standard deviation of 10 days. The North Carolina zoo is very excited to discover that all 4 of its female zebras have just started pregnancies. They must be ready to provide a dietary supplement on each day of the pregnancy for each zebra. Let Y be the random variable for the total number of dietary supplements that the zoo will have to provide. All zebra pregnancies at the zoo may be assumed to have independent lengths. a) What are the mean and standard deviation of Y? Give your answer to the nearest whole number. ?Y ____= dietary supplements ?Y ____= dietary supplements b) The zoo currently has 1125 supplements on hand (they were expecting some pregnancies, perhaps). What is the probability that they will need to buy more supplements to accommodate these zebras? Give your answer to 3 decimal places. P(Y > 1125)
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!
The length of a zebra pregnancy (from conception to birth) varies according to a
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