Assume that the amount of weight that male college students gain during their freshman year are normally distributed with a. Mean of u= 1.3 kg and a standard deviation of o= 4.4 kg If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3kg during freshman year.If 4 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? A.Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. B.Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. C.Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size. D.Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.

Mean of u= 1.3 kg and a standard deviation of σ= 4.4 kg

Answered: If 1 male college student is randomly…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Assume that the amount of weight that male college students gain during their freshman year are normally distributed with a. Mean of u= 1.3 kg and a standard deviation of o= 4.4 kg

If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3kg during freshman year.

If 4 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.

Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size.

Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.

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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