The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the weights of these loaves varies. The mean weight is 0.8 lb. and 3 oz., or 448 grams. Assume the standard deviation of the weights is 23 grams and a sample of 43 loaves is to be randomly selected. What is the probability that the sample mean will have a value less than 439? (Give your answer correct to four decimal places.) What is the probability that the sample mean will be within 6 grams of the mean? (Give your answer correct to four 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!
The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the weights of these loaves varies. The
What is the probability that the sample mean will have a value less than 439? (Give your answer correct to four decimal places.)
What is the probability that the sample mean will be within 6 grams of the mean? (Give your answer correct to four decimal places.)
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