A Machine That Fills Cans With Soda Fills According

'Soda cans A motorcar that fills cans with soda fills co-ordinate to Normal model with mean 12.i ounces and standard deviation 0.05 ounces_ a) If the cans claim to have 12 ounces of soda each, what percentage of cans are under-filled? ) Management wants to ensure that only 1% of cans are under-filled. Scenario ane: If the hateful fill up of the cans remains at 12.ane ounces, what standard departure does the filling machine demand to have to achieve this goal? ii. Scenario 2: If the standard deviation is to remain at 0.05 ounces, what hateful does the filling car need t0 have to reach this goal?'

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Answer

The fill book of an automated filling automobile used for filling cans of carbonated drinkable is normally distributed with a mean of 12.4 fluid ounces and a standard deviation of 0.i fluid ounce. (a) What is the probability that a make full volume is less than 12 fluid ounces? (b) If all cans less than 12.1 or greater than 12.6 ounces are scrapped, what proportion of cans is scrapped? (c) Determine specifications that are symmetric about the mean that include $99 \%$ of all cans.

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Video Transcript

right. The random variable is ordinarily distributed with me and new equals 12.iv. And standard difference sigma equals 0.1. Based on this information we want to answer eight receive alot. This question is evaluating our understanding of normal distributions and normally distributed random variables. That's all Nosotros rely on. The following relevant information. First and the normal random variable Z z people maps the schools and probabilities. The example hither shows that in that location probably is a greater than zero equals peanut corresponds to an area under the standard normal distribution to the correct of that Xena we tin can also exercise is the scores less than some donuts. Nosotros rely on a symmetry and total surface area of a standard normal assault specifically though because we take a random variable, that is not easy but rather 10 we have to make the conversion to a standard normal equally equals ten minus mu over sigma. This conversion volition allow united states to answer a few. Run across below. So first, starting with a the probably the X is less than 12 is converting to a Z score the same as the probability Z is less than four. So because we're looking for the probability is less than four rather than probably is he is greater than four. The solution to this problem will be rather than zero, approximately one. This is because of the score of four is quite big and then it is nearly all of the area nether this. Nether normal that is to the left. Then next if we eliminate all Ten less than 12.1 and all Ten greater than 12.vi. What proportion is eliminated? This political party that nosotros want to answer? What is the area under the normal curve? To the left? And 12.1 is the 1.six. For standard normal converting to Z scores br formula nosotros have the wonderful negative three and Z ii equals ii. That'south the probability is the left of the i cluster. Probably like shooting fish in a barrel, greater than C. Two which is 2.241. Finally. To answer part C. We want to answer within what values Plus Ten 99% of all samples. So nosotros're looking for the probability that Z is between plus or minus nothing equals 00.9. This is the not equal plus or minus 2.56. That's converting to 10 past inverting our formula here for Z. Nosotros accept X equals not sigma plus mu or Myu plus or minus two. Sigma equals 12.144. 12.656.

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