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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 0.4 ounces. 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, do it. If not, explain why you cannot. (b) A quality control inspector measures the contents of an SRS of 50 cans of the company's soda and calculates the sample mean
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 0.4 ounces. 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, do it. If not, explain why you cannot. (b) A quality control inspector measures the contents of an SRS of 50 cans of the company's soda and calculates the sample mean
Theprobabilitythat a singlerandomlyselected can contain 11.9 ounces or less is 0.179.B. The probability that a randomly selected can contain 11.9 ounces or less can be calculated using the normaldistribution. Specifically, we can use the Cumulative Distribution Function (CDF) to find the probability that a randomly selected can will contain 11.9 ounces or less.We know that the mean of the cans is 12 ounces with a standard deviation of 0.4 ounces. We can use the Z-score to calculate the probability. TheZ-scoreis equal to (11.9 - 12) / 0.4 = -0.25. We then use the Z-score to calculate the probability.Specifically, we can use the CDF to calculate the probability that a randomly selected can will contain 11.9 ounces or less. The CDF for the normal distribution is given byP(X ≤ x) = ½[1 + erf(x - μ/σ√2)].When we plug in the Z-score of -0.25 into the equation, we getP(X ≤ 11.9) = ½[1 + erf(-0.25)] = 0.179. Therefore, the probability that a single randomly selected can contain 11.9 ounces or less is 0.179.For the qualitycontrolinspector, we can use the sample mean to calculate the probability that the cans will contain 11.9 ounces or less. Specifically, if the sample mean is 11.9 ounces or less, then the probability that the cans will contain 11.9 ounces or less is 1.If thesample meanis greater than 11.9 ounces, then we can use the normal distribution to calculate the probability. Specifically, we can use the Z-score to calculate the probability. The Z-score is equal to (11.9 - sample mean) / 0.4. We then use the Z-score to calculate the probability using the CDF.For more questions likeProbabilityclick the link below:brainly.com/question/11234923#SPJ4...