The following table lists the mean and standard deviation of several different normal distributions. For each, a sample of 20 individuals was taken, as well as a sample of 50 individuals. For each sample, calculate the probability that the mean of the sample was less than the given value Y. The table displays statistical data for different conditions, with the following columns:1. **Mean**: The average value of the distribution. - Values: -5, 10, -55, 122. **Standard Deviation**: A measure of the amount of variation or dispersion of a set of values. - Values: 5, 30, 20, 33. **Y**: A specified value for comparison. - Values: -5.2, 8, -61, 12.54. **n=20, Pr(Ȳ < Y)**: Probability that the sample mean (Ȳ) is less than the specific value (Y) when the sample size is 20. - Values: ?5. **n=50, Pr(Ȳ < Y)**: Probability that the sample mean (Ȳ) is less than the specific value (Y) when the sample size is 50. - Values: ?The probabilities for each condition are currently unspecified, indicated by question marks. These probabilities would be calculated based on the normal distribution using the provided means, standard deviations, sample sizes (n=20 and n=50), and Y values.

The table for mean and standard deviation is: Mean (µ) Standard Deviation (σ) Y -5 5…

Answered: The following table lists the mean and…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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The following table lists the mean and standard deviation of several different normal distributions. For each, a sample of 20 individuals was taken, as well as a sample of 50 individuals. For each sample, calculate the probability that the mean of the sample was less than the given value Y.

The table displays statistical data for different conditions, with the following columns:

1. **Mean**: The average value of the distribution.
- Values: -5, 10, -55, 12

2. **Standard Deviation**: A measure of the amount of variation or dispersion of a set of values.
- Values: 5, 30, 20, 3

3. **Y**: A specified value for comparison.
- Values: -5.2, 8, -61, 12.5

4. **n=20, Pr(Ȳ < Y)**: Probability that the sample mean (Ȳ) is less than the specific value (Y) when the sample size is 20.
- Values: ?

5. **n=50, Pr(Ȳ < Y)**: Probability that the sample mean (Ȳ) is less than the specific value (Y) when the sample size is 50.
- Values: ?

The probabilities for each condition are currently unspecified, indicated by question marks. These probabilities would be calculated based on the normal distribution using the provided means, standard deviations, sample sizes (n=20 and n=50), and Y values.

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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