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Answer to Question #91572 in Statistics and Probability for fahad
Question #91572
Q5. A machine is set to fill cereal boxes with a mean weight of 500 grams of cereal per box. The standard deviation is known to be 25 grams. A random sample of 100 filled boxes is taken and the mean weight of cereal per box is computed as 504 grams. Is there reason to
believe that machine is over filling the boxes use a = 0.05
believe that machine is over filling the boxes use a = 0.05
Expert's answer
"P(\\bar{X}>504)=P(Z>\\frac{504-500}{\\frac{25}{\\sqrt{100}}})=P(Z>1.6)=1-P(Z<1.6)=1-0.9452=0.0548."
Since the probability that a random sample of 100 filled boxes has the mean weight 504 g or more is greater than 0.05,
there is no reason to believe that machine is over filling the boxes.
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Comments
Dear Muhammad Fahad Fayyaz, please use the panel for submitting new questions.
The weights of packages filled by machine are normally distributed about a mean of 25 ounces, with a standard deviation of one ounce. What is the probability that n packages from the machine will have an average weight of less than 24 ounces if n = 1, 4, 16, 64? (10)
Dear Sean, please use the panel for submitting new questions.
The can filling machine was very accurate, with an average filling weight of 400g and a standard deviation of 20g. The operations manager takes a random sample of 50 cans and finds that the sample mean filling weight is 395g. a) What is the probability of obtaining a sample mean of 395g or less?
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