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
XVWLTE (98o 335)
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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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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