Answered: Assume that the duration of human…

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

Assume that the duration of human pregnancies can be described by a normal model with mean 269 days and standard deviation11 days. Complete parts a) through d) below.

a) What percentage of pregnancies should last between 255 and 270 days?

b) At least how many days should the longest 20% of all pregnancies last?

c) Suppose a certain obstetrician is currently providing prenatal care to 40pregnant women. Let y represent the mean length of their pregnancies. According to the central limit theorem, what is the mean and standard deviation SD(y) of the normal model of the distribution of the sample mean, y? The mean is ? SD(y)=?

d) What is the probability that the mean duration of these patients' pregnancies will be less than 266 days?

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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