In 2021, the CDC estimated the mean height of U.S. women aged 20 years old and over was 63.5 inches with a standard deviation of 5.2 inches. (https://www.cdc.gov/nchs/fastats/body-measurements.htm)What is the expected mean for a sample of 150 women?What is the standard deviation of the mean for a sample of 150 women?What is the probability of 150 women having a sample mean below 60 inches?What is the probability of 150 women having a sample mean above 65 inches?What is the probability of 200 women having a sample mean below 60 inches? Notice the change in sample size.What is the probability of 200 women having a sample mean above 65 inches?

Given that:The population mean height of U.S. women: inches and The population standard deviation: inches1) Given that, the sample size: womenWe know the property that the expected value of the sample mean is an unbiased estimator of the population mean.So, the expected mean for a sample of women is inches.2) Given that, the sample size: womenThe standard deviation of the sample mean for a sample of size is calculated using the formula:So, the standard deviation of the sample mean is .The z-score formula is given as follows:3) Given that, the sample size: womenThe probability of women having a sample mean below inches is calculated as follows:The cumulative probability of the standard normal variate is obtained using the Excel function as follows: "=NORM.S.DIST(-8.2435, TRUE)".So, the probability of women having a sample mean below inches is .4) Given that, the sample size: womenThe probability of women having a sample mean above inches is calculated as follows:The cumulative probability of the standard normal variate is obtained using the Excel function as follows: "=1-NORM.S.DIST(3.5329, TRUE)".So, the probability of women having a sample mean above inches is .5) Given that, the sample size: womenThe probability of women having a sample mean below inches is calculated as follows:The cumulative probability of the standard normal variate is obtained using the Excel function as follows: "=NORM.S.DIST(-9.5187, TRUE)".So, the probability of women having a sample mean below inches is .6) Given that, the sample size: womenThe probability of women having a sample mean above inches is calculated as follows:The cumulative probability of the standard normal variate is obtained using the Excel function as follows: "=1-NORM.S.DIST(4.0795, TRUE)".So, the probability of women having a sample mean above inches is .1) The expected mean for a sample of women is inches.2) The standard deviation of the sample mean is .3) The probability of women having a sample mean below inches is .4) The probability of women having a sample mean above inches is .5) The probability of women having a sample mean below inches is .6) The probability of women having a sample mean above inches is .

Answered: In 2021, the CDC estimated the mean…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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In 2021, the CDC estimated the mean height of U.S. women aged 20 years old and over was 63.5 inches with a standard deviation of 5.2 inches. (https://www.cdc.gov/nchs/fastats/body-measurements.htm)

What is the expected mean for a sample of 150 women?
What is the standard deviation of the mean for a sample of 150 women?
What is the probability of 150 women having a sample mean below 60 inches?
What is the probability of 150 women having a sample mean above 65 inches?
What is the probability of 200 women having a sample mean below 60 inches? Notice the change in sample size.
What is the probability of 200 women having a sample mean above 65 inches?

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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