Answered: rding to the article "Are Babies…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

According to the article "Are Babies Normal?" by Traci Clemons and Marcello Pagano published in The American Statistician, Vol. 53, No. 4, pp. 298-302, the birth weights of babies are normally distributed with a mean of 3352 grams and a standard deviation of 598 grams.

a) What is the probability that a randomly selected baby weighs between 1558 grams and 5146 grams? Be sure to use the Empirical Rule and not exact values, and round your z-scores to the nearest whole number. Round your answer to 4 decimal places.

b) Write about and check each of the conditions needed in the context of this situation to use the Central Limit Theorem

Conditions:

c) What is the probability that the average weight of 10 randomly selected babies is between 3541.1 grams and 3730.21 grams? Be sure to use the Empirical Rule and not exact values, and round your z-scores to the nearest whole number. Round your answer to 4 decimal places.

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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