Milk Although most of us buy milk by the quart orgallon, farmers measure daily production in pounds.Ayrshire cows average 47 pounds of milk a day, witha standard deviation of 6 pounds. For Jersey cows, themean daily production is 43 pounds, with a standarddeviation of 5 pounds. Assume that Normal modelsdescribe milk production for these breeds.a) We select an Ayrshire at random. What’s the probabilitythat she averages more than 50 pounds of milk a day?b) What’s the probability that a randomly selected Ayrshiregives more milk than a randomly selected Jersey?c) A farmer has 20 Jerseys. What’s the probability thatthe average production for this small herd exceeds45 pounds of milk a day?d) A neighboring farmer has 10 Ayrshires. What’s theprobability that his herd average is at least 5 poundshigher than the average for part c’s Jersey herd?
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!
Milk Although most of us buy milk by the quart or
gallon, farmers measure daily production in pounds.
Ayrshire cows average 47 pounds of milk a day, with
a standard deviation of 6 pounds. For Jersey cows, the
mean daily production is 43 pounds, with a standard
deviation of 5 pounds. Assume that Normal models
describe milk production for these breeds.
a) We select an Ayrshire at random. What’s the probability
that she averages more than 50 pounds of milk a day?
b) What’s the probability that a randomly selected Ayrshire
gives more milk than a randomly selected Jersey?
c) A farmer has 20 Jerseys. What’s the probability that
the average production for this small herd exceeds
45 pounds of milk a day?
d) A neighboring farmer has 10 Ayrshires. What’s the
probability that his herd average is at least 5 pounds
higher than the average for part c’s Jersey herd?
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