Out of 1 1 point point 3 points points 79 in rounded

[1 out of 1]
[1
point] point]
7 of 9 ID: MST.CPD.ND.03.0060
A group of mutual funds earned varying annual rates of return in the last year. These rates of return are normally
distributed with a mean of 7% and a standard deviation of 20%.
One mutual fund in this group managed to earn a rate of return that was double that of this group's average that
year. This performance would put the fund in the top X% of those funds in that year.
Calculate X%. Give your answer to 1 decimal place.
=
79 in
Rounded as last step
%
[3
points] points]
8 of 9 ID: MST.NDM.MPD.04.0010
The Mean Corporation has two major franchise operations each with many
outlets across the country: a coffee house franchise and a fast food franchise.
For both franchises, a statistician has collected and analyzed data for the annual
profits of the outlets. Figures for the means and standard deviations are
presented in the table below.
Franchise
Mean
($)
Standard
deviation
($)
Coffee 286,500 40,500

[3 out of 3]
John Q owns both a coffee and fast food franchise. His annual profit for the coffee house is $391,800 and his annual
profit for the fast food franchise is $690,600.
Calculate the standardized values for both franchises. Give your answer rounded to 1 decimal place.
Coffee standardized value =
2.6
Fast food standardized value =
1.8
Relative to the rest of the outlets in each group, John's coffee franchise is performing
better
than his fast
food franchise.
Feedback
You are correct.
You are correct.
Discussion
The standardized value is a measure of the number of standard deviations by which a value deviates from the
mean. When given two values from separate populations the most objective method of comparing them is to
calculate their standardized value. The value that is highest relative to their own population is the value which
has the highest standardized value.
Coffee franchise
The standardized value can be calculated using the following formula: show variables
z =
x - μ
σ
=
391,800 - 286,500
40,500
=
105,300
40,500
= 2.6
Fast food franchise
The standardized value can be calculated using the following formula: show variables
z =
x - μ
σ
=
690,600 - 516,000
97,000
=
174,600
97,000
= 1.8
a)
b)
a)
b)
a)