Answered: According to data from the U.S. Army…

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 data from the U.S. Army the average foot length of women as normally distributed with a mean of 9.6 inches and a standard deviation of 0.5 inches.

Find P95 (that is the top 5% of women’s foot length)

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 + ...

Expert Solution

Step 1

The random variable x represents foot lengths of women.

x follows normal distribution with a mean of 9.6 inches and a standard deviation of 0.5 inches. The notation P₉₅ is the foot length of women that separates the bottom 95% and top 5%.

That is, P₉₅ represents the area of 0.95 to the left of x and the area of 0.05 to the right of x

Use Table: Standard normal (z) distribution to find P₉₅.

Procedure:

Locate the area of 0.95 in the body of the A-2 table.
Move left until the first column and note the value as 1.6.
Move upward until the top row is reached and note the values as 0.04 and 0.05.

The z score is,

$\begin{array}{rcl} Z 0.01 & = & \frac{1.64 + 1.65}{2} \\ = & \frac{3.29}{2} \\ = & 1.645 \end{array}$

Thus, the z score is 1.645.

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