5 A bottling machine can be regulated so that it discharges an average of u ounces per bottle. It has been observed that the amount of fill dispensed by the machine is normally distributed with o = 1.0 ounce. If asample of n = 9 filled bottles is randomly selected from the output of the machine on a given day (all bottled with the same machine setting), and the ounces of fill are measured for each, then the probability thatthe sample mean will be within 0.35 ounce of the true mean is 0.7063. Suppose that Y is to be computed using a sample of size n.(a) If n = 16, what is P(|Y – µl < 0.35)? (Round your answer to four decimal places.)(b) Find P(|Y – ul < 0.35) when Y is to be computed using samples of sizes n = 25, n = 36, n = 49, and n = 64. (Round your answers to four decimal places.)P(\Y – ul s 0.35)P(IY - µl s 0.35)n = 25n = 36n = 49P(IY – µl s 0.35)n = 64P(|Y – ul s 0.35) =(c) What pattern do you observe among the values for P(|Y - ul < 0.35) that you observed for the various values of n?O The probabilities increase as n increases.O The probabilities stay the same as n increases.O The probabilities decrease as n increases.(d) It can be shown that a sample of size n = 32 is needed if we wish Y to be within 0.35 ounce of u with probability 0.95. Do the results that you obtained in part (b) seem to be consistent with that?O No, these results are not consistent since the probability is less than 0.95 for values of n greater than 32.O Yes, these results are consistent since the probability is less than 0.95 for values of n greater than 32.O No, these results are not consistent since the probability is greater than 0.95 for values of n greater than 32.O Yes, these results are consistent since the probability is greater than 0.95 for values of n greater than 32.

Given : Y~N(μ,σ2=1)Let,Y¯~Nμ,σn2=1n2Let,Z=Y¯-μσn~N(0,1)

A bottling machine can be regulated so that it discharges an average of u ounces per bottle. It has been observed that the amount of fill dispensed by the machine is normally distributed with o = 1.0 ounce. If a sample of n = 9 filled bottles is randomly selected from the output of the machine on a given day (all bottled with the same machine setting), and the ounces of fill are measured for each, then the probability that the sample mean will be within 0.35 ounce of the true mean is 0.7063. Suppose that Y is to be computed using a sample of size n. (a) If n = 16, what is P(IY - µl S 0.35)? (Round your answer to four decimal places.) (b) Find P(IY - ul s 0.35) when Y is to be computed using samples of sizes n = 25, n = 36, n = 49, and n = 64. (Round your answers to four decimal places.) P(IY - µl s 0.35) = P(IY - µl s 0.35) = P(IY - ul s 0.35) = P(IỸ - µl s 0.35) = n= 25 n = 36 n = 49 n = 64 (c) What pattern do you observe among the values for P(IY - µl s 0.35) that you observed for the various values of n? O The probabilities increase as n increases. O The probabilities stay the same as n increases. O The probabilities decrease as n increases. (d) It can be shown that sample of sizen = 32 is needed if we wish Y to be within 0.35 ounce of u with probability 0.95. Do the results that you obtained in part (b) seem to be consistent with that? O No, these results are not consistent since the probability is less than 0.95 for values of n greater than 32. O Yes, these results are consistent since the probability is less than 0.95 for values of n greater than 32. O No, these results are not consistent since the probability is greater than 0.95 for values of n greater than 32. O Yes, these results are consistent since the probability is greater than 0.95 for values of n greater than 32.

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....