W3 Written Assignment “Week 3 Assignment”
Business Statistics
Week 3 Assignment
Question 1
Seventy percent of the students applying to a university are accepted. Using the binomial
probability tables or Excel, what is the probability that among the next 18 applicants:
1.
2.
3.
4.
5.
6.
At least 6 will be accepted?
Exactly 10 will be accepted?
Exactly 5 will be rejected?
Fifteen or more will be accepted?
Determine the expected number of acceptances.
Compute the standard deviation.
Question 2
Scores on a recent national statistics exam were normally distributed with a mean of 80 and a
standard deviation of 6.
1. What is the probability that a randomly selected exam will have a score of at least 71?
2. What percentage of exams will have scores between 89 and 92?
3. If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an
award?
W3 Discussion “The Normal Probability Dist.”
Business Statistics
The Normal Probability Distribution
In §6.2 we are introduced to the Normal Probability Distribution and the special case of the
Normal Probability Distribution, the Standard Normal Probability Distribution, which is a
Normal Probability Distribution with mean (u) zero and variance (σ2) one.
One way to find probabilities from a Standard Normal Distribution is to use probability tables,
which are located inside the front cover of your textbook.
•
•
According to the table, what is the probability when z ≤ -1.75? The probability when z ≤
1.75?
What properties of probability distributions and specifically the Normal Probability
Distribution do you notice from the two probabilities that you have found in the table?
W3 Project Assignment “Project Week 3”
Business Statistics
Project Week 3
For these project assignments throughout the course you will need to reference the data in the
ROI Excel spreadsheet.
Using the ROI data set:
1. If we select 7 colleges from a major and then record whether they are of ‘School Type’
‘Private’ or not, is this experiment a binomial one? Why or why not?
2. For each of the 2 majors determine if the ‘Annual % ROI’ appears to be normally
distributed. Consider the shape of the histogram and the measures of central tendency
(mean and median) to justify your results. Report on each of these with charts and
calculations to justify your answers.
Question 1
1. A numerical description of the outcome of an experiment is called a
descriptive statistic
probability function
variance
random variable
Question 2
1. A random variable that can assume only a finite number of values is referred to as a(n)
infinite sequence
finite sequence
discrete random variable
discrete probability function
Question 3
1. A random variable that may take on any value in an interval or collection of intervals is
known as a
continuous random variable
discrete random variable
continuous probability function
finite probability function
Question 4
1. A description of the distribution of the values of a random variable and their associated
probabilities is called a
probability distribution
random variance
random variable
expected value
Question 5
1. The expected value for a binomial probability distribution is
E(x) = Pn(1 - n)
E(x) = P(1 - P)
E(x) = nP
E(x) = nP(1 - P)
Question 6
1. The variance for the binomial probability distribution is
var(x) = P(1 - P)
var(x) = nP
var(x) = n(1 - P)
var(x) = nP(1 - P)
Question 7
1. Which of the following is not a characteristic of an experiment where the binomial
probability distribution is applicable?
the experiment has a sequence of n identical trials
exactly two outcomes are possible on each trial
the trials are dependent
the probabilities of the outcomes do not change from one trial to another
Question 8
1. The number of electrical outages in a city varies from day to day. Assume that the
number of electrical outages (x) in the city has the following probability distribution.
x f(x)
0 0.80
1 0.15
2 0.04
3 0.01
The mean and the standard deviation for the number of electrical outages (respectively)
are
2.6 and 5.77
0.26 and 0.577
3 and 0.01
0 and 0.8
Question 9
1. The center of a normal curve is
always equal to zero
is the mean of the distribution
cannot be negative
is the standard deviation
Question 10
1. A normal distribution with a mean of 0 and a standard deviation of 1 is called
a probability density function
an ordinary normal curve
a standard normal distribution
none of these alternatives is correct
Question 11
1. A negative value of Z indicates that
the number of standard deviations of an observation is to the right of the mean
the number of standard deviations of an observation is to the left of the mean
a mistake has been made in computations, since Z cannot be negative
the data has a negative mean
Question 12
1. Which of the following is not a characteristic of the normal probability distribution?
The mean, median, and the mode are equal
The mean of the distribution can be negative, zero, or positive
The distribution is symmetrical
The standard deviation must be 1
Question 13
1. Z is a standard normal random variable. The P (1.41 ≤ Z ≤ 2.85) equals
0.4978
0.4207
0.9185
0.0771
Question 14
1. X is a normally distributed random variable with a mean of 8 and a standard deviation of
4. The probability that X is between 1.48 and 15.56 is
0.0222
0.4190
0.5222
0.9190
Question 15
1. Larger values of the standard deviation result in a normal curve that is
shifted to the right
shifted to the left
narrower and more peaked
wider and flatter
School Type
Private
Private
Private
Public
Private
Public
Private
Private
Private
Private
Private
Private
Private
Private
Private
Public
Public
Private
Private
Private
Best College ROI by Majo 2013: Payscale.com
Cost
$222,700.00
$176,400.00
$212,200.00
$125,100.00
$212,700.00
$92,910.00
$214,900.00
$217,800.00
$225,600.00
$217,300.00
$226,500.00
$215,500.00
$223,500.00
$226,600.00
$189,300.00
$89,700.00
$87,030.00
$218,200.00
$229,900.00
$148,800.00
30 Year ROI
$1,786,000.00
$1,758,000.00
$1,714,000.00
$1,535,000.00
$1,529,000.00
$1,501,000.00
$1,485,000.00
$1,483,000.00
$1,444,000.00
$1,442,000.00
$1,441,000.00
$1,438,000.00
$1,428,000.00
$1,414,000.00
$1,397,000.00
$1,382,000.00
$1,376,000.00
$1,343,000.00
$1,339,000.00
$1,321,000.00
Annual ROI
7.70%
8.40%
7.80%
9.10%
7.40%
10.10%
7.30%
7.20%
7.00%
7.10%
7.00%
7.20%
7.00%
7.00%
7.50%
9.90%
10.00%
6.90%
6.70%
8.10%
School Type
Private
Private
Private
Private
Private
Public
Private
Private
Public
Private
Public
Private
Public
Private
Public
Public
Public
Public
Private
Public
Cost
$221,700.00
$213,000.00
$230,100.00
$222,600.00
$225,800.00
$87,660.00
$224,900.00
$221,600.00
$125,100.00
$215,700.00
$92,530.00
$217,800.00
$89,700.00
$229,600.00
$101,500.00
$115,500.00
$104,500.00
$69,980.00
$219,400.00
$64,930.00
30 Year ROI
Annual ROI
$2,412,000.00
8.70%
$2,064,000.00
8.30%
$1,949,000.00
7.90%
$1,947,000.00
8.00%
$1,938,000.00
8.00%
$1,937,000.00
11.20%
$1,915,000.00
7.90%
$1,878,000.00
7.90%
$1,854,000.00
9.80%
$1,794,000.00
7.90%
$1,761,000.00
10.60%
$1,752,000.00
7.70%
$1,727,000.00
10.70%
$1,716,000.00
7.50%
$1,703,000.00
10.20%
$1,694,000.00
9.70%
$1,690,000.00
10.10%
$1,685,000.00
11.50%
$1,676,000.00
7.60%
$1,668,000.00
11.70%
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