Solution Found!
Refer to Exercise 7.9. Assume now that the amount of fill
Chapter 7, Problem 10E(choose chapter or problem)
Refer to Exercise 7.9. Assume now that the amount of fill dispensed by the bottling machine is normally distributed with \(\sigma=2\) ounces.
If \(\mathrm{n}=9\) bottles are randomly selected from the output of the machine, what is
\(\mathrm{P}(|\bar{Y}-\mu| \leq .3)\)? Compare this with the answer obtained in Example 7.2.
Find \(\mathrm{P}(|\bar{Y}-\mu| \leq .3)\) when \(\bar{Y}\) is to be computed using samples of sizes\(n=25, n=36, n=49, \text { and } n=64\)
What pattern do you observe among the values for \(\mathrm{P}(|\bar{Y}-\mu| \leq .3)\) that you observed for the various values of n?How do the respective probabilities obtained in this problem (where \(\sigma=2\)) compare to those obtained in Exercise 7.9 (where \(\sigma=1\))?Equation Transcription:
Text Transcription:
\sigma=2
n=9
P (|\bar Y-\mu| \leq .3)
P (|\bar Y-\mu| \leq .3)
\bar Y
n=25, n=36, n=49, and n=64
P (|\bar Y-\mu| \leq .3)
\sigma=2
\sigma=1
Questions & Answers
QUESTION:
Refer to Exercise 7.9. Assume now that the amount of fill dispensed by the bottling machine is normally distributed with \(\sigma=2\) ounces.
If \(\mathrm{n}=9\) bottles are randomly selected from the output of the machine, what is
\(\mathrm{P}(|\bar{Y}-\mu| \leq .3)\)? Compare this with the answer obtained in Example 7.2.
Find \(\mathrm{P}(|\bar{Y}-\mu| \leq .3)\) when \(\bar{Y}\) is to be computed using samples of sizes\(n=25, n=36, n=49, \text { and } n=64\)
What pattern do you observe among the values for \(\mathrm{P}(|\bar{Y}-\mu| \leq .3)\) that you observed for the various values of n?How do the respective probabilities obtained in this problem (where \(\sigma=2\)) compare to those obtained in Exercise 7.9 (where \(\sigma=1\))?Equation Transcription:
Text Transcription:
\sigma=2
n=9
P (|\bar Y-\mu| \leq .3)
P (|\bar Y-\mu| \leq .3)
\bar Y
n=25, n=36, n=49, and n=64
P (|\bar Y-\mu| \leq .3)
\sigma=2
\sigma=1
ANSWER:Step 1 of 5
Given:
The amount of the fill dispensed by the bottling machine is normally distributed.
The population standard deviation is 