MATH 533 Week 8 Final Exam 2. Questions With Answers. Latest.1. (TCO A) Seventeen salespeople reported the following number of sales calls completed last
... [Show More] month.
72 93 82 81 82 97 102 107 119
86 88 91 83 93 73 100 102
a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on
number of sales calls per month.
b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33)
a.
Ans: Mean, median, mode, and standard deviation, Q1, Q3, Min, and 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 and 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” and resides in an urban location.
Ans: P(is considered “good” and 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 = 1p = 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+0.0008 =
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 and 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 = (2200027009)/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 and 23,000 gallons for a
given day.
Ans:
z score for 20000 gallons = (2000027009)/4530 = 1.547
From the Standard Normal cumulative proportions
p value = 0.0606
z score for 23000 gallons = (2300027009)/4530 = 0.885
From the Standard Normal cumulative proportions
p value = 0.1880
probability that the demand for gasoline falls between 20,000 and 23,000 gallons for a given day =
(0.18800.0606) = 0.1274
c. How many gallons of gasoline should be on hand at the beginning of each day so that we can meet
the demand 90% of the time (i.e., the station stands a 10% chance of running out of gasoline for that
day)? (Points : 18)
Ans: For the demand to be met 90 % of the time, it means that
pvalue = 0.9
Zscore for (pvalue = 0.9) = 1.28
gallons of gasoline should be on hand = 1.28*4530 + 27009 = 32807.4 gallons ~ approx 32808
gallons
5. (TCO C) An operations analyst from an airline company has been asked to develop a fairly
accurate estimate of the mean refueling and baggage handling time at a foreign airport. A random
sample of 36 refueling and baggage handling times yields the following results.
Sample Size = 36
Sample Mean = 24.2 minutes
Sample Standard Deviation = 4.2 minutes
a. Compute the 90% confidence interval for the population mean refueling and baggage time. [Show Less]