Yogurt is sold in cartons labeled as containing 6 ounces, but the actual contents vary slightly from container to container. Suppose that the content distribution is approximately normal in shape with a mean of 6 ounces and a standard deviation of 0.05 ounces. a. Would it be unusual to observe a container weighing 6.2 ounces? Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution. b. What proportion of cartons has actual contents less than 5.95 ounces? Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution. the label states that each container will contain 6 ounces and we know that the standard deviation is 0.05 ounces. The quality control group is ok having 5% of the Yogurt containers containing a bit too much and 5% of containers containing a bit too little. Hence, they want to know the cutoffs that define the middle 90% of the Yogurt containers. Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution.
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!
Yogurt is sold in cartons labeled as containing 6 ounces, but the actual contents vary slightly from container to container. Suppose that the content distribution is approximately normal in shape with a mean of 6 ounces and a standard deviation of 0.05 ounces.
a. Would it be unusual to observe a container weighing 6.2 ounces? Explain your answer using the appropriate statistics and a correctly labeled and shaded
b. What proportion of cartons has actual contents less than 5.95 ounces? Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution.
the label states that each container will contain 6 ounces and we know that the standard deviation is 0.05 ounces. The quality control group is ok having 5% of the Yogurt containers containing a bit too much and 5% of containers containing a bit too little. Hence, they want to know the cutoffs that define the middle 90% of the Yogurt containers.
Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution.
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