1. Statistics 2500 Fall 2015, Section 001 Assignment #1
Due Date: Wednesday, Nov. 04, 2015
Assignment Requirement:
a) The some data sets are available on the course website www.math.mun.ca/~hongwm/S2500.
b) Please staple the pages of your assignment together.
c) Write your name and student number and lab section number on a cover page of your
assignment.
d) Drop the completed assignment into the designated Assignment Box on or before the due
date.
Assignment Questions:
1. The following data represent the approximate retail price (in $) and the energy cost per year
(in $) of 15 refrigerators:
Model Price Energy Cost
Maytag MTB1956GE 825 36
Kenmore 7118 750 43
Maytag MTB2156GE 850 39
Kenmore Elite 1000 38
Amana ART2107B 800 38
GE GTS18KCM 600 40
Kenmore 7198 750 35
Frigidaire Gallery GLHT216TA 680 38
Kenmore 7285 680 40
Whirlpool Gold GR9SHKXK 940 37
Frigidaire Gallery GLRT216TA 680 40
GE GTS22KCM 650 44
Whirlpool ETF1TTXK 800 43
Whirlpool Gold GR2SHXK 1050 40
Frigidaire FRT18P5A 510 40
You can obtain the data for R on the course website. The data is in the file fridge.txt.
Answer the following.
a) Construct a histogram of the price of refrigerators.
b) Based on (a), would you expect the mean to be about the same, less than or greater than
the median? Explain.
c) Find the sample mean and median price of refrigerators.
d) Find the standard deviation and range of the price.
2. The data contained in the file cereal.txt consists of the cost in dollar per ounce, calories, fiber
in grams and sugar in grams for 33 breakfast cereals. You can obtain the data for R on the
course website. The data is in the file cereal.txt.
a) Construct a stem-and-leaf display of the fiber in the cereals. Describe its shape.
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2. b) Would we be able to apply the empirical rule to help understand the standard deviation
of the amount of fiber in the cereals? Explain.
c) Find the mean and median number of calories in the cereal, as well as the standard
deviation.
3. Consider the following observations: {3, 6, 2, -1, -4, 4, 9, 8}
a) Find the sample mean, median, variance and standard deviation of the data.
b) Add 3 to each of the original observations, and repeat (a). How do your answers
compare to those in (a)?
c) Multiply each of the original observations by 4.5, and repeat (a). How do your answers
compare to those in (a)?
4. Consider the following data on the results of the Sept. 9, 2006 Lotto 6/49 draw (of course, no
statistics student would ever buy a lottery ticket!).
Regular Numbers Bonus | Numbers Matched Prize Values Number of Winners
=============================================================================================
13 22 31 32 34 48 26 | 6 $14,284,257 0
| 5 + Bonus $441,409.10 1
| 5 $2,430.90 150
| 4 $76.20 9067
| 3 $10.00 176083
| 2 + Bonus $5.00 127346
=============================================================================================
a) Find the sample mean of the prize value awarded.
Hint: If we wrote the prizes in a long list, the number 14284257 would appear zero times,
441409.10 would appear 1 time, down to 5 appearing 127346 times.
b) The price of a Lotto 6/49 ticket is $2. Your answer in (a) is larger than $2. Since the mean
(average) prize value awarded is greater than the cost of the ticket, does this mean we
should buy a Lotto 6/49 ticket? Explain.
5. A study of tourists who visit St. John's found that 55% visit Signal Hill, 44% visit Cape Spear
and 36% visit both locations.
a) What is the probability that a tourist will visit Signal Hill or Cape Spear?
b) What is the probability that a tourist only visits Signal Hill?
c) Given that a tourist visits Cape Spear, what is the probability they visit Signal Hill?
6. TV viewers were asked to rate the overall quality of television shows from 0 (terrible) to 100
(the best). The results are below:
40 43 44 47 48 49 49 49 61 62 65 66 76 79 50 51 51 52 53 54 89 55
a) Construct a stem-and-leaf plot of the data. Describe its shape.
b) Find the median of the ratings.
c) First try to explain how the mean rating would compare to the median you found in (b)
without calculating the mean, and verify your answer buy actually calculate the mean
out.
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3. 7. The data in the file pizza.txt represent the cost of a slice of pizza in dollars, number of
calories per slice, and amount of fat in grams per slice for a sample of 36 pizza products. You
can obtain the data for R in the Date Files folder on the course website.
a) Construct a histogram of the amount of fat per pizza slice.
b) Construct a stem-and-leaf plot of the number of calories per slice.
c) Find the sample mean and median price of the pizza slices.
d) Would we be able to apply the empirical rule to help understand the standard deviation
of the cost of the pizza slices? Explain.
8. The manufacturer of a lie detector claims that it is 98% accurate. The St. John's police
department isn't convinced, so they ask the manufacturer to test its machine on four suspects.
Assume the suspects' responses are independent.
a) Assume that the manufacturer's claim is true. What is the probability that the lie detector
will correctly determine the truth for all four suspects?
b) Assume that the manufacturer's claim is true. What is the probability that the lie detector
will yield an incorrect result for at least one of the four suspects?
9. A local bakery has determined a probability distribution for the number of cheesecakes that
they sell in during lunch hour on a given day. The distribution is as follows:
Number sold (X) 0 1 2 3 4
P(X) 0.05 0.20 ? 0.35 0.10
a) What is the probability that they sell 2 cheesecakes?
b) What is the probability that they sell more than 3 cheesecakes?
c) Find the mean number of cheesecakes sold, and the standard deviation.
10. The manager of a computer network has developed the following probability distribution of
the number of interruptions per day:
Interruptions (X) 0 1 2 3 4 5 6
P(X) 0.32 0.35 0.18 0.08 0.04 0.02 0.01
Answer the following.
a) Construct a graph of the probability distribution.
b) Compute the expected number of interruption per day
c) Compute the standard deviation of interruption per day
11. A poll found that 73% of households own digital cameras. A random sample of 9 households
is selected.
a) What is the probability that 2 of the households own a digital camera?
b) What is the probability that at most 1 of households owns a digital camera?
c) What is the probability that at least 1 household owns a digital camera?
d) Find the mean number and the standard deviation of households that own a digital
camera.
e) Now suppose a random sample of 450 households is selected. Use R to find the
probability that at least 350 own a digital camera.
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