The weights of bags of frozen vegetables packaged at a factory are normally distributed with a mean weight of 3.43 lbs anda standard deviation of 1.41 lbs. For quality control purposes, a random sample of 14 bags is chosen once per day, andweighed. Let X be the random variable representing the mean weight of the bags.a. Fill in the blank, rounding your answers to 2 decimal places if needed. According to the Central Limit Theorem, X isapproximately normal with a mean oflbs and a standard error of the meanlbs.b. Find the z-score associated to a sample with a mean of 3.88 lbs, using the sampling distribution. Round your answer totwo decimal places.c. Find the probability that a randomly selected sample of 14 bags has a mean weight higher than 3.88 lbs. Round youranswer to 4 decimal places.d. Find the probability that a randomly selected individual bag has a weight higher than 3.88 lbs. Round your answer to 4decimal places.e. The machine that fills the bag will be pulled for inspection and repairs if the sample mean of the quality control sample isin the bottom 3% or top 3% of possible sample means. What sample average weights will trigger a repair? Round youranswers to 2 decimal places.The machine will be pulled for repairs if the quality control sample has a mean weight belowlbs.lbs or above

It is given that; x follows normal distribution with mean µx = 3.43 cm and the standard deviation of…

Answered: weights of bags of frozen vegetables…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A CNC (computer numerical control) machine produces iron automobile crankshafts. Samples are measured and the inner diameter are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 centimeters. For all computations, assume an approximately normal distribution. The sample mean and standard deviation for the given data are = 1.0056, and s =0.0246. Find a 99% confidence interval on the mean of diameter. Compute a 99% prediction interval on a measured diameter of a single crankshaft piece taken from the machine. Find the 99% tolerance limits that will contain most of the metal pieces produced by the CNC machine. O a. CI on the mean: 0.9781 <µ <1.0331. Prediction Interval: 0.9186 s Xp+151.0926. Tolerance Interval (0.8937 and 1.1175) O b. Insufficient data to compute. Missing the sample size n Oc CIon the mean: 0.9781 <µ<1.0331. Prediction Interval: 0.9186 s Xp+151.0926. Tolerance Interval (0.8937 and 1.1175). Insufficient data to compute for the Tolerance Interval Od. CI on…
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