A brand of water-softener salt comes in packages marked net weight 40 lb. The company that packages the salt claims that the bags contain an average of 40 lb of salt and that the standard deviation of the weights is 1.51 lb. Assume that the weights are normally distributed. a. Obtain the probability that the weight of one randomly selected bag of water-softener salt will be 391b or less if the company’s claim is true. b. Determine the probability that the mean weight of 10 randomly selected bags of water-softener salt will be 39 lb or less if the company’s claim is true. c. If you bought 10 bags of water-softener salt and their mean weight was less than 39 lbs, would you consider this evidence that the company’s claim is incorrect? Explain your answer.
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!
A brand of water-softener salt comes in packages marked net weight 40 lb. The company that packages the salt claims that the bags contain an average of 40 lb of salt and that the standard deviation of the weights is 1.51 lb. Assume that the weights are
a. Obtain the
b. Determine the probability that the
c. If you bought 10 bags of water-softener salt and their mean weight was less than 39 lbs, would you consider this evidence that the company’s claim is incorrect? Explain your answer.
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