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MATH 533 Week 8 Final Exam Set 1
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MATH 533 Week 8 Final Exam Set 1
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Week 8 : Final Exam - FinalExam Page 1
1. (TCO A) Seventeen salespeople reported the following number of sales calls completed last month.
72 93 82 81 82 97 102 107 119
86 88 91 83 93 73 100 102
a. Compute the mean, median, mode, & standard deviation, Q1, Q3, Min, & Max for the
above sample data on number of sales calls per month.
b. In the context of this situation, interpret the Median, Q1, & Q3. (Points : 33)
a.
Ans: Mean, median, mode, & standard deviation, Q1, Q3, Min, & Max for the above
sample data on number of sales calls per month
Mean 91.23529412
Median 91
Mode 93
Standard
Deviation 12.37704232
1st quartile 82.00
3rd quartile 100.00
Minimum 72
Maximum 119
b. Median of the above sales calls means that if all the sales calls data points are
arranged in an ascending order, then 91 Nos. of calls made would fall in the
middle. So, there are as 8 sales calls data point above this median & 8 sales calls
data point below this median point.
Q1 is the first quartile points which is 82 nos. of calls made. It means that there
are 25 % of sales calls data point which lie below this point.
Q3 is the third quartile points which is 100 nos. of calls made. It means that there
are 75 % of sales calls data point which lie below this point.
2. (TCO B) Cedar Home Furnishings has collected data on their customers in terms of
whether they reside in an urban location or a suburban location, as well as rating the
customers as either “good,” “borderline,” or “poor.” The data is below.
Urban Suburban Total
Good 60 168 228
Borderline 36 72 108
Poor 24 40 64
Total 120 280 400
If you choose a customer at random, then find the probability that the customer
a. is considered “borderline.”
, Ans: P(Customer is considered “borderline) = 108/400 = 27/100
b. is considered “good” & resides in an urban location.
Ans: P(is considered “good” & resides in an urban location) = 60/400 = 3/20
c. is suburban, given that customer is considered “poor.” (Points : 18)
Ans: P(is suburban, given that customer is considered “poor”) = 40/64 =5/8
3. (TCO B) Historically, 70% of your customers at Rodale Emporium pay for their
purchases using credit cards. In a sample of 20 customers, find the probability that
a. exactly 14 customers will pay for their purchases using credit cards.
Ans:
This is a binomial distribution with p = 0.70, so q = 1-p = 0.30
n = 20
Probability distribution:
P(exactly 14 customers will pay for their purchases using credit cards) = 20 C 14
*(0.70)^14 *(0.30)^6 = 0.19164
b. at least 10 customers will pay for their purchases using credit cards.
Ans :
0.0308+0.0653+0.1144+0.1643+0.1916+0.1788+0.1304+0.0716+0.0278+0.0068+0.0
008 = 0.9826
c. at most 12 customers will pay for their purchases using credit cards.
(Points : 18)
Ans:
0.00000000003+0.000000002+0.00000004+0.0000005+0.000005+0.00003+0.0002+0
.0010+0.0038+0.0120+0.0308+0.0653+0.1144 = 0.2275
4. (TCO B) The demand for gasoline at a local service station is normally distributed with
a mean of 27,009 gallons per day & a standard deviation of 4,530 gallons per day.
a. Find the probability that the demand for gasoline exceeds 22,000 gallons for
a given day.
Ans:
z- score = (22000-27009)/4530 = -1.1057395
From the Standard Normal cumulative proportions
p- value = 0.1346
probability that the demand for gasoline exceeds 22,000 gallons for a given day = 1-
0.1346 = 0.8654
b. Find the probability that the demand for gasoline falls between 20,000 &
23,000 gallons for a given day.
Ans:
z- score for 20000 gallons = (20000-27009)/4530 = -1.547
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