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Excel Probability & Stats Homework: Events, Gender, Marital Status & Normal Dist. - Prof. , Assignments of Business Statistics

Homework problems for business statistics (busa 3101) class, focusing on probability theory and statistics. Students are required to answer questions related to events a, b, c, and d, gender and marital status of customers, and normal distribution using microsoft excel. Questions cover probability calculations, mutual exclusivity, independence, and expected values.

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Pre 2010

Uploaded on 08/04/2009

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Business Statistics (BUSA 3101) Dr. L. Arjomand
Chapters 4-6 Homework Problems. Due Date: Will be announced by the faculty
INSTRUCTIONS: Answer all of the following seven (7) questions by using Microsoft Excel as
much as possible. Your answers should be precise and you should give a brief explanation
(interpretation) of your answers. Please print your name and question number(s) on the answer
sheet(s). When you use Microsoft Excel, you should provide me with the Excel outputs.
Assignments are due in the class on the dates which will be announced by the faculty. Do not
fax, and/or e-mail your finished assignment to the instructor. Do not leave your finished
assignment in my mail box and/or on my office door.
_____________________________________________________________________
1. You are given the following information on Events A, B, C, and D.
P(A) = .4 P(A D) = .6 P(A C) = .04
P(B) = .2 P(AB) = .3 P(A D) = .03
P(C) = .1
a. Compute P(D).
b. Compute P(A B).
c. Compute P(AC).
d. Compute the probability of the complement of C.
e. Are A and B mutually exclusive? Explain your answer.
f. Are A and B independent? Explain your answer.
g. Are A and C mutually exclusive? Explain your answer.
h. Are A and C independent? Explain your answer.
2. A bank has the following data on the gender and marital status of 200 customers.
Male Female
Single 20 30
Married 100 50
a. What is the probability of finding a single female customer?
b. What is the probability of finding a married male customer?
c. If a customer is female, what is the probability that she is single?
d. What percentage of customers is male?
e. If a customer is male, what is the probability that he is married?
f. Are gender and marital status mutually exclusive?
g. Is marital status independent of gender? Explain using probabilities.
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Download Excel Probability & Stats Homework: Events, Gender, Marital Status & Normal Dist. - Prof. and more Assignments Business Statistics in PDF only on Docsity!

Business Statistics (BUSA 3101) Dr. L. Arjomand

Chapters 4-6 Homework Problems. Due Date: Will be announced by the faculty

INSTRUCTIONS: Answer all of the following seven (7) questions by using Microsoft Excel as

much as possible. Your answers should be precise and you should give a brief explanation

(interpretation) of your answers. Please print your name and question number(s) on the answer

sheet(s). When you use Microsoft Excel, you should provide me with the Excel outputs.

Assignments are due in the class on the dates which will be announced by the faculty. Do not

fax, and/or e-mail your finished assignment to the instructor. Do not leave your finished

assignment in my mail box and/or on my office door.

_____________________________________________________________________

1. You are given the following information on Events A, B, C, and D.

P(A) = .4 P(A ∪ D) = .6 P(A ∩ C) =.

P(B) = .2 P(A⎮B) = .3 P(A ∩ D) =.

P(C) =.

a. Compute P(D). b. Compute P(A ∩ B). c. Compute P(A⎮C). d. Compute the probability of the complement of C. e. Are A and B mutually exclusive? Explain your answer. f. Are A and B independent? Explain your answer. g. Are A and C mutually exclusive? Explain your answer. h. Are A and C independent? Explain your answer.

2. A bank has the following data on the gender and marital status of 200 customers.

Male Female Single 20 30 Married 100 50

a. What is the probability of finding a single female customer? b. What is the probability of finding a married male customer? c. If a customer is female, what is the probability that she is single? d. What percentage of customers is male? e. If a customer is male, what is the probability that he is married? f. Are gender and marital status mutually exclusive? g. Is marital status independent of gender? Explain using probabilities.

  1. The probability of an economic decline in the year 2001 is 0.23. There is a probability of 0.64 that we will elect a republican president in the year 2000. If we elect a republican president, there is a 0.35 probability of an economic decline. Let “D” represent the event of an economic decline, and “R” represent the event of election of a Republican president.

a. Are “R” and “D” independent events? b. What is the probability of electing a Republican president in 2000 and an economic decline in the year 2001? c. If we experience an economic decline in the year 2001, what is the probability that a Republican president will have been elected in the year 2000? d. What is the probability of economic decline in 2001 or a Republican president elected in the year 2000 or both?

  1. In a large university, 15% of the students are female. If a random sample of twenty students is selected, a. what is the probability that the sample contains exactly four female students? b. what is the probability that the sample will contain no female students? c. what is the probability that the sample will contain exactly twenty female students? d. what is the probability that the sample will contain more than nine female students? e. what is the probability that the sample will contain fewer than five female students? f. what is the expected number of female students?
  2. A manufacturing company has 5 identical machines that produce nails. The probability that a machine will break down on any given day is 0.1. Define a random variable x to be the number of machines that will break down in a day. a. What is the appropriate probability distribution for x? Explain how x satisfies the properties of the distribution. b. Compute the probability that 4 machines will break down. c. Compute the probability that at least 4 machines will break down. d. What is the expected number of machines that will break down in a day? e. What is the variance of the number of machines that will break down in a day?
  3. The average starting salary for this year's graduates at a large university (LU) is $30,000 with a standard deviation of $8,000. Furthermore, it is known that the starting salaries are normally distributed. a. What is the probability that a randomly selected LU graduate will have a starting salary of at least $30,400? b. Individuals with starting salaries of less than $15,600 receive a low income tax break. What percentage of the graduates will receive the tax break? c. What are the minimum and the maximum starting salaries of the middle 95% of the LU graduates? d. If 303 of the recent graduates have salaries of at least $43,120, how many students graduated this year from this university?
  4. Z is the standard normal random variable. Use Excel to calculate the following: a. P( z ≤ 2.5) b. P(0 ≤ z ≤ 2.5) c. P(-2 ≤ z ≤ 2) d. P( z ≤ -0.38) e. P( z ≥ 1.62) f. z value with .05 in the lower tail g. z value with .05 in the upper tail