Question

SHOW ALL WORK PLEASE I'LL RATE THUMBS UPS The State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices, such as scales, are accurate so customers and businesses are not cheated. Periodically, employees of the department go to businesses and test their scales. For example, a dairy bottles milk in 1-gallon containers. Suppose that if the filling process is working correctly, the mean volume of all gallon containers is 1.00 gallon is normally distributed with a mean of 1 gallon and with a standard deviation equal to 0.10 gallon 1. what is the probability that a randomly selected bottle of milk from the population has a weight less than 0.90 gallons? 2. Random sample of 16 bottles what is the probability that the mean weight for sample will be less than 0.95 gallons? 3. If selecting sample of 25 batttles what is the probability that mean weight for the sample will be less than 0.95 gallons? 4. Why does probabilities in parts 1, 2 and 3 decrease as sample size increase? 5. If mean weight of random sample of 16 gallons of milk selected by inspector falls below 0.90 gallons the company is fine. Suppose the weight of all gallons container is normal distributed, and standard deviation of 0.10 gallon can't change. Company decides to increase mean fill level of gallons to limit the probability of getting to no more than 0.001 what should this mean fill level be?

Answer 1

e the dauy hetile mk XnN,0.12) P(x0.9) P(X- 0-9- 0 1 P -1) PIz) 0.84134 O 15866 2) dd be the enget of 16 footles meam N( 0.12 0-95 P(X-P 0.95- 0.1/16 xく く-2 1 - P(2) 0.97725 O.02275

ght25 hetle 11 be the meam O.12 N 25 O.95-1 0-1/J35 P( 0.95) = - P -2.5) P( <2.5). IO.99379 O.00621 poabely 8ambl size Ths habbems because the emeale As the decueaues sample sizedeucus the stadaud diucton hance makumg the pob saller ca sdue ondy thugpelity Soy beox ad a tuma