Answered: PROBLEM: A large corporation has…

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

PROBLEM:

A large corporation has thousands of employees. The distribution of annual salaries for the employees is skewed to the right, with a mean of $68,000 and a standard deviation of $18,000. Because business has been good this year, the CEO of the company decides that very employee will receive a $5000 bonus. Let X be the current annual salary of a randomly selected employee before the bonus and Y be the employee's salary after the bonus. Describe the shape, center, and variability of the probability distribution of Y.

PROBLEM:

Employees selling refrigerators at an appliance store make money on commission based on how many refrigerators they sell. The number of refrigerators R sold in a randomly selected hour has the following probability distribution:

Here is a histogram of the probability distribution along with the mean and standard deviation.

At this appliance store, the commission earned is $30 for each refrigerator sold. That is, if C = total commission earned for a randomly selected hour, C = 30R.

(a) What shape does the probability distribution of C have?

(b) Find the mean of C.

PROBLEM:

In a large introductory statistics class, the distribution of scores on a recent test follows an approximately Normal distribution with a mean of 82.4 and a standard deviation of 5.1. Let X be the test score for a randomly selected student. To test the students' grasp of the material, the teacher cleverly decides to convert all the scores to z-scores and then report these values to students. If Z is the z-score for the randomly selected student, then

Z=(X-82.4)/5.1

(a) Find the mean of Z.

(b) Calculate and interpret the standard deviation of Z.

* probabilit
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Section 6.2 Alternate Examples
EXILS CLGGIC
ALTERNATE EXAMPLE (page 384)
Everyone gets a bonus
Effect of adding/subtracting a constant
PROBLEM:
per
A large corporation has thousands of employees. The distribution of annual salaries for the
employees is skewed to the right, with a mean of $68,000 and a standard deviation of
$18,000. Because business has been good this year, the CEO of the company decides that
every employee will receive a $5000 bonus. Let X be the current annual salary of a
randomly selected employee before the bonus and Y be the employee's salary after the
bonus. Describe the shape, center, and variability of the probability distribution of Y.
aoismsl blo-
ALTERNATE EXAMPLE (page 385)
Selling cars
wwollat
Effect of multiplying/dividing by a constantog eE lo noltal
30 bon
PROBLEM:
18 rue
Employees selling refrigerators at an appliance store make money on commission based on
how many refrigerators they sell. The number of refrigerators R sold in a randomly
selected hour has the following probability distribution:
Number of
0 1 2 3 4 5
refrigerators
Probability
0.22 0.31 0.12 0.25 0.08 0.02
Here is a histogram of the probability distribution along with the mean and standard
deviation.

(b) Describe P(X>0) in w ds and find its value.
ty.
30-
0.25
0.20
0.15
a10
00'0
0 1
2 3 4 5
R = Number of refrigerators sold
HR= 1.72
%3D
OR= 1.36
At this appliance store, the commission earned is $30 for each refrigerator sold. That is, if C
= total commission earned for a randomly selected hour, C = 30R.
(a) What shape does the probability distribution of C have?
(b) Find the mean of C.
(c) Calculate the standard deviation of C.
20
ALTERNATE EXAMPLE (387)
What z-score did I get?
Analyzing the effect of transformations
PROBLEM:
In a large introductory statistics class, the distribution of scores on a recent test follows an
approximately Normal distribution with a mean of 82.4 and a standard deviation of 5.1. Let
X be the test score for a randomly selected student. To test the students' grasp of the
material, the teacher cleverly decides to convert all the scores to z-scores and then report
these values to students. If Z is the z-score for the randomly selected student, then
X-82.4
5.1
(a) Find the mean of Z.
(b) Calculate and interpret the standard deviation of Z.

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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