The weight of an energy bar is approximately normally distributed with a mean of 42.90 grams with a standard deviation of 0.045 gram. Explain the difference in the results of (a) and (c). Part (a) refers to an individual bar, which can be thought of as a sample with sample size ___. Therefore, the standard error of the mean for an individual bar is ___ times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a) that is ___A____ the probability in part c. A: smaller than, larger than or the same as? (a). What is the probability that an individual energy bar weighs less than 42.865 grams? Answer: 0.218 (c): If a sample of 25 energy bars is selected, what is the probability that the sample mean weight is less than 42.865 grams? Answer: 0.001
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 weight of an energy bar is approximately
Explain the difference in the results of (a) and (c).
Part (a) refers to an individual bar, which can be thought of as a sample with
A: smaller than, larger than or the same as?
(a). What is the probability that an individual energy bar weighs less than 42.865 grams? Answer: 0.218
(c): If a sample of 25 energy bars is selected, what is the probability that the sample mean weight is less than 42.865 grams? Answer: 0.001
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