The body weight of 500 students in Grade 12 are approximately normally distributed with a mean of 72.9 kilograms and standard deviation of 5 kilograms. If 100 students are randomly sampled:determine the mean and standard error of the sampling distribution of the sample meanfind the probability that the sample mean falls between 71 and 73 kilogramsthe number of sample means that is above 80 kilograms

Given,sample size(n)=100mean(μ)=72.9standard deviation(σ)=5

Answered: The body weight of 500 students in…

A First Course in Probability (10th Edition)

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ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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The body weight of 500 students in Grade 12 are approximately normally distributed with a mean of 72.9 kilograms and standard deviation of 5 kilograms. If 100 students are randomly sampled:

determine the mean and standard error of the sampling distribution of the sample mean
find the probability that the sample mean falls between 71 and 73 kilograms
the number of sample means that is above 80 kilograms

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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