ITM 207 Lecture Notes - Lecture 7: Standard Deviation, Random Variable, Quartile
12 May 2018
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1
Review Questions for Final Exam.
1. Classify the following variables into a) qualitative or quantitative 2) Numerical or
categorical 3) Nominal, ordinal, interval or ratio
i) College type: State, Public, Private ii) Number of full time graduates in a university
iii) Percentage of students applied for each course
iv) Marital status ( single, married, divorced, other) v) Home ownership ( own, rent,
other) vi) College grade point average vii) Product rating ( 1 = excellent, 2 = good, 3 =
fair, 4 = poor, 5 = very good) viii) Gender ix) Income x) Age
2) The following data represent the total fat (g) for some burgers and chicken items from
a sample of fast-food chains.
Burgers
19 31 34 35 39 39 43
Chicken
7 9 15 16 16 18 22 25 27 33 39
For the burgers and chicken items separately:
a) Compute the mean, median, mode, maximum, minimum, range, first quartile, third
quartile, standard deviation, and coefficient of variation. (Burgers: 34.29, 35, 39, 43, 19,
24, 31, 39, 7.8, 22.7% ; Chicken: 20.64, 18, 16, 39, 7, 32, 15, 27, 9.77, 47.3%)
b) Compute two box plots for the two items. Are there any suspect outliers or outliers?
(Burgers: Five-number summary: 19, 31, 35, 39, 43, IQR = 8, LIF = 19, LOF = 7,
RIF = 51, ROF = 63, No suspect outliers or outliers. Chicken: Five-number
summary: 7, 15, 18, 27, 39, IQR = 12, LIF = -3, LOF = -21, RIF = 45, ROF = 63, No
suspect outliers or outliers.)
c) Discuss the skewness of the two graphs. (Burgers: Med. – min. = 16, Max. – med. =
8, Q1 – min. = 12, Max. – Q3 = 4, med. – Q1 = 16, Q3 – med. = 4, Chicken: Med. –
min. = 11, Max. – med. = 21, Q1 – min. = 8, Max. – Q3 = 12, med. – Q1 = 3, Q3 –
med. = 9, The data for burgers are skewed to the left and the data for chicken items
are skewed to the right)
d) In general, what item has more fat? (In general, burgers have more fat than chicken
items.)
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e) What item is more variable in terms of fat? (Use 10% rule for the CVs)
f) What is the least total fat among burgers? Is this number higher than 50% of the total
fat among chicken items? ( 19, yes)
g) What is the highest total fat among chicken items? Do burgers have higher total fat
than this number? (39, yes)
3) The manager of a computer repair center wants to know whether he can offer his
customers a guarantee of all computer repairs within 4 days. His past records are based
on the following probability distribution.
Number of days
Probability
1
0.15
2
0.25
3
0.3
4
0.18
5
0.12
a) Calculate the mean number of days his customers wait for a computer repair. (2.87)
b) Calculate the standard deviation of repair time. (1.22)
c) Based on your computations, can the manager reach his goal? Why? (Yes, his past
records show that his average repair time is close to 3 days)
4) An advertising company believes that for an ad campaign to be successful, at least
80% of those seeing a television commercial must be able to recall the name of the
company one hour after viewing it. The company plans to show the commercial to a
random sample of 20 people.
a) Assuming that the advertisement will be successful, what is the expected number of
people in the sample who will recall the company name one hour after viewing? (16)
b) What is the probability of 11 or fewer people being able to recall the name? (0.001)
c) Based on your results, what conclusion might the company make about this ad
campaign? (since this probability is very small and not close to the success rate of the
population, i. e. 80%, the ad campaign will not be successful)
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5) A company experiences product returns at the rate of 2 per month with the number of
product returns distributed as a Poisson random variable. Determine the probability that
next month there will be
a) no returns (0.1353)
b) two returns (0.2707)
c) more than 2 returns (0.3233)
d) In the last 3 months, the company had only 1 month in which the number of returns
was at most 2. What will you tell the company concerning the maximum return rate in the
last 3 months? (we are 68% confident that the return rate had not exceeded 2 in the
last 3 months)
6) A random variable (X) is normally distributed with a mean of 25 and a standard
deviation of 5.
a) Find the probability that X is less than 27.
b) What value will 10% of the observations be below?
c) Determine 2 values of which the smallest has 25% of the values below it and the
largest has 25% of the values above it.
7) A designer of maternity wear sells dresses and pants priced around $ 150 each for an
average total sale of $ 1200. The total sale has a normal distribution with a standard
deviation of $ 350.
a) Calculate the probability that a random selected customer will have a total sale of more
than $ 1500. (0.1957)
b) Compute the probability that that the total sale will be within 2 standard deviations of
the mean total sales. (0.9545)
c) Determine the median total sale. ($ 1200)
8) The time to get an oil change at a certain car dealership averages 42.3 minutes with a
standard deviation of 8.6 minutes.
a) There are 45 cars booked for oil changes today. What is the probability that the jobs
can be done in an average of 38 minutes or less? (0.0004)
b) Suppose 90 oil changes were done in one particular week. There is a 95% chance that
the mean time was more than ……… minutes. (40.8)
9) The manager of a cereal-filling process in a large factory claims that, on average, its
machines deviate from a perfect filling by an average of 30g in a month, with a standard
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