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…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 7E

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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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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