Answered: Normal distribution. Assume the height…

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

Normal distribution. Assume the height of female 20-29 year-old is normally
distributed with a mean of 65 inches and a standard deviation of 3 inches.
a. What is the probability that a randomly selected girl 20-29 year-old will be 67 inches or
lower?
b. What is the probability that a randomly selected girl 20-29 year-old will be 67 inches or
higher?
c. What is the probability that a randomly selected girl 20-29 year-old will be between 63 and
70 inches?
Suppose a random sample of four 20-29 year-old females is selected.
d. What is the probability that all four will be 67 inches or lower?
e. What is the distribution of the sample mean height of 4 females? Provide all info.
x bar ~ ____________________(___________________,____________________ )
The distribution is [Circle One:] Exact Approximate
Why? _________________________________________________________________
f. What is the probability that the mean height of four will be 66 inches or higher?

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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