A certain beverage company is suspected of underfilling its cans of soft drink. The company advertises that its cans contain, on average, 12 ounces of soda with standard deviation 0.35 ounce. For the questions that follow, suppose that the company is telling the truth. (a) Can you calculate the probability that a single randomly selected can contains 11.9 ounces or less? If so, find the probability. If not, explain why you cannot. (b) A quality control inspector measures the contents of a random sample of 100 cans of the company’s soda and calculates the sample mean . What is the shape, mean and standard deviation of the sampling distribution of for samples of size n = 100? (c) The inspector in part (b) obtains a sample mean of 11.9 ounces. Calculate the probability that a random sample of 100 cans produces a sample mean amount of 11.9 ounces or less. (you do NOT have to do the full State/Plan/Do/Conclude here) (d) Given that the inspector found an average of 11.9 ounces in their sample, and the probability of that result that you found in part (c) (assuming the company is being truthful), would you conclude that the company is telling the truth about how much soda is in each can? Justify 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 certain beverage company is suspected of underfilling its cans of soft drink. The company advertises that its cans contain, on average, 12 ounces of soda with standard deviation 0.35 ounce. For the questions that follow, suppose that the company is telling the truth.
(a) Can you calculate the
(b) A quality control inspector measures the contents of a random sample of 100 cans of the company’s soda and calculates the sample
(c) The inspector in part (b) obtains a sample mean of 11.9 ounces. Calculate the probability that a random sample of 100 cans produces a sample mean amount of 11.9 ounces or less. (you do NOT have to do the full State/Plan/Do/Conclude here)
(d) Given that the inspector found an average of 11.9 ounces in their sample, and the probability of that result that you found in part (c) (assuming the company is being truthful), would you conclude that the company is telling the truth about how much soda is in each can? Justify your answer.
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