Answer To: The monthly average sales of the Smiling Ninja Computer Company may be approximated to a normal...
Robert answered on Dec 22 2021
Question 1. (6 marks)
The monthly average sales of the Smiling Ninja Computer Company may be
approximated to a normal distribution curve. It has a mean of $23,000 and a
standard deviation of $3,500.
Drawing a curve for each question, calculate the proportions of the following:
a. The proportion of sales greater than $21,500 per month; (2 marks)
Let,
X = average sales of the Smiling Ninja Computer Company ~Normal($23,000,
$3,5002)
So,
Z =
~Normal(0,1); and we can find the probability associated with Z
from the standard normal distribution table.
Here,
P(X > 21500) = 1-P(X < 21500) = 1- (Z <
) = 1-P(Z < - 0.42857)
The graph is given below,
0.4
0.3
0.2
0.1
0.0
X
D
e
n
s
it
y
-0.42857
0.6659
0
Distribution Plot
Normal, Mean=0, StDev=1
From the graph, the required proportion is 66.59%.
b. The proportion of sales less than $20,500 per month; (2 marks)
Here,
P(X< 20500) = P(Z < -0.7142857)
The required graph is given below,
0.4
0.3
0.2
0.1
0.0
X
D
e
n
s
it
y
-0.714286
0.2375
0
Distribution Plot
Normal, Mean=0, StDev=1
From the graph, the required proportion is 23.75%.
c. The proportion of sales between $22,500 and $25,000. (2 marks)
P(22500 = P(Z < 0.57142857) – P(Z < -0.142857)
0.4
0.3
0.2
0.1
0.0
X
D
e
n
s
it
y
-0.142857
0.2729
0.571429
Distribution Plot
Normal, Mean=0, StDev=1
So the required proportion is 27.29%
Question 2. (4 marks)
a. What is a “Chi-Squared Test”? Provide a fully referenced explanation. (2
marks)
Chi-squared test means those kinds of tests where the test statistic follows a
Chi-sq distribution so we can use a Chi-sq distribution to test the hypothesis.
The most common examples are 1-sample variance test and Chi-sq
goodness of fit.
But...