The amount of water in a bottle is approximately normally distributed with a mean of 2.55 liters with a standard deviation of 0.025 liter. Complete parts (a) through (e) below. 9. The amount of water in a bottle is approximately normally distributed with a mean of 2.55 liters with astandard deviation of 0.025 liter. Complete parts (a) through (e) below.a. What is the probability that an individual bottle contains less than 2.53 liters?(Round to three decimal places as needed.)b. If a sample of 4 bottles is selected, what is the probability that the sample mean amount contained isless than 2.53 liters?(Round to three decimal places as needed.)c. If a sample of 25 bottles is selected, what is the probability that the sample mean amount contained isless than 2.53 liters?(Round to three decimal places as needed.)d. Explain the difference in the results of (a) and (c).Part (a) refers to an individual bottle, which can be thought of as a sample with sample sizeTherefore, the standard error of the mean for an individual bottle istimes the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a)that is (1).(Type integers or decimals. Do not round.)the probability in part (c).e. Explain the difference in the results of (b) and (c).The sample size in (c) is greater than the sample size in (b), so the standard error of the mean (or thestandard deviation of the sampling distribution) in (c) is (2)than in (b). As the standarderror (3)values become more concentrated around the mean. Therefore, the probabilitywhen thethat the sample mean will fall close to the population mean will always (4)sample size increases.(1)larger thanlessdecreases,(4)increasethe same asgreaterincreases,decreasesmaller than

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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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The amount of water in a bottle is approximately normally distributed with a mean of 2.55 liters with a standard deviation of 0.025 liter. Complete parts (a) through (e) below.

9. The amount of water in a bottle is approximately normally distributed with a mean of 2.55 liters with a
standard deviation of 0.025 liter. Complete parts (a) through (e) below.
a. What is the probability that an individual bottle contains less than 2.53 liters?
(Round to three decimal places as needed.)
b. If a sample of 4 bottles is selected, what is the probability that the sample mean amount contained is
less than 2.53 liters?
(Round to three decimal places as needed.)
c. If a sample of 25 bottles is selected, what is the probability that the sample mean amount contained is
less than 2.53 liters?
(Round to three decimal places as needed.)
d. Explain the difference in the results of (a) and (c).
Part (a) refers to an individual bottle, which can be thought of as a sample with sample size
Therefore, the standard error of the mean for an individual bottle is
times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a)
that is (1).
(Type integers or decimals. Do not round.)
the probability in part (c).
e. Explain the difference in the results of (b) and (c).
The sample size in (c) is greater than the sample size in (b), so the standard error of the mean (or the
standard deviation of the sampling distribution) in (c) is (2)
than in (b). As the standard
error (3)
values become more concentrated around the mean. Therefore, the probability
when the
that the sample mean will fall close to the population mean will always (4)
sample size increases.
(1)
larger than
less
decreases,
(4)
increase
the same as
greater
increases,
decrease
smaller than

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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