The weight of an energy bar is approximately normally distributed with a mean of 42.9042.90 grams with a standard deviation of 0.0350.035 gram. Complete parts (a) through (e) below. Question content area bottom Part 1 a. What is the probability that an individual energy bar weighs less than 42.87542.875 grams? enter your response here (Round to three decimal places as needed.) Part 2 b. If a sample of 44 energy bars is selected, what is the probability that the sample mean weight is less than 42.87542.875 grams? enter your response here (Round to three decimal places as needed.) Part 3 c. If a sample of 2525 energy bars is selected, what is the probability that the sample mean weight is less than 42.87542.875 grams? enter your response here (Round to three decimal places as needed.) Part 4 d. Explain the difference in the results of (a) and (c). Part (a) refers to an individual bar, which can be thought of as a sample with sample size enter your response here. Therefore, the standard error of the mean for an individual bar is enter your response here times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a) that is ▼ larger than the same as smaller than the probability in part (c). (Type integers or decimals. Do not round.) Part 5 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 ▼ less greater than in (b). As the standard error ▼ decreases, increases, values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always ▼ increase decrease when the sample size increases.

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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Question content area bottom

Part 1

a. What is the probability that an individual energy bar weighs less than

42.87542.875

grams?

enter your response here

(Round to three decimal places as needed.)

Part 2

b. If a sample of

energy bars is selected, what is the probability that the sample mean weight is less than

42.87542.875

grams?

enter your response here

(Round to three decimal places as needed.)

Part 3

c. If a sample of

2525

energy bars is selected, what is the probability that the sample mean weight is less than

42.87542.875

grams?

enter your response here

(Round to three decimal places as needed.)

Part 4

d. Explain the difference in the results of (a) and (c).

Part (a) refers to an individual bar, which can be thought of as a sample with sample size

enter your response here.

Therefore, the standard error of the mean for an individual bar is

enter your response here

times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a) that is

▼

larger than

the same as

smaller than

the probability in part (c).

(Type integers or decimals. Do not round.)

Part 5

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

▼

less

greater

than in (b). As the standard error

▼

decreases,

increases,

values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always

▼

increase

decrease

when the sample size increases.

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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