15. 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 = sample of n = the machine on a given day (all bottled with the same machine setting) and the ounces of fill measuered for each. :1 ounce. A 9 filled bottles is randomly selected from the output of a) Find the probability that the sample mean will be within 0.3 ounce of the true mean for that particular setting. b) How many observations should be included in the sample if we wish X to be within 0.3 ounce of u with probability 0.95? c) Suppose we plan to select a random sample of ten bottles and measure the amount of fill in cach bottle. If these ten observations are used to calculate S2, find numbers bị and b2 such that P(b < S < b2) = 0.90.

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15. 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 ounce. 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 measuered for each.
a) Find the probability that the sample mean will be within 0.3
ounce of the true mean for that particular setting.
b) How many observations should be included in the sample if we
wish X to be within 0.3 ounce of u with probability 0.95?
c) Suppose we plan to select a random sample of ten bottles and
measure the amount of fill in cach bottle. If these ten observations
are used to calculate S2, find numbers b and b2 such that
P(b < S2 <b2) = 0.90.
Transcribed Image Text:4 BEST pdf Chapter 6-Matrix Algebraj Stats Inference.pdf ers/TSEPISO%20OMAJARA/Desktop/Certificate%20in%20Statistics/YEAR%202%202019-2020/FIRST%20SEMESTER/ST2505/ST2501%20Exeraise% No results < > Options v 15. 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 ounce. 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 measuered for each. a) Find the probability that the sample mean will be within 0.3 ounce of the true mean for that particular setting. b) How many observations should be included in the sample if we wish X to be within 0.3 ounce of u with probability 0.95? c) Suppose we plan to select a random sample of ten bottles and measure the amount of fill in cach bottle. If these ten observations are used to calculate S2, find numbers b and b2 such that P(b < S2 <b2) = 0.90.
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