Answered: The lengths of pregnancies are normally…

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

The lengths of pregnancies are normally distributed with a mean of 267 days and a standard
deviation of 15 days.
(a) Find the probability that an individual woman has a pregnancy shorter than 259 days.
(b) If 36 women are randomly selected, find the probability that they have a mean preg-
nancy shorter than 259 days.
(c) There should be a difference in your method for the previous two questions. Explain
what you did differently for each problem and explain WHY your answers are different.
(d) Find the probability that an individual woman has a pregnancy longer than 295 days.
(e) Find the probability that an individual woman has a pregnancy between 259 and 295
days.
(f) What is the cutoff number of days for a pregnancy for the top 15% of women?
(g) What is the cutoff number of days for a pregnancy for the bottom 25% of women?

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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