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Problem 1)
A book inventory record contains the following information:
a) Title: More Mysteries --- nominal
b) Author: Roger Mortimer --- nominal
c) Date of publication: 1998 ---- interval
d) List price: $25.00 --- ratio
e) Number in stock: 6 --- ratio
For the information (a) to (e) list the highest level of measurement as ratio, interval,
ordinal, or nominal.
Problem 3)
To determine monthly rental prices of apartment units in San Francisco Bay area,
samples were constructed in the following ways. Identify the technique used to produce
each sample. (cluster, convenience, random, stratified, systematic):
a) Number all the units in the area and use a random number table to select the
apartments to include in the sample. –
random
b) Classify the apartment units according to the number of bedrooms and then
take a random sample from each of the classes. -stratified
c) Classify the apartments according to zip code and take a random sample from
each of the zip code regions.
stratified
d) Look in the newspaper and choose the first apartments you find that list rents.
Convenience
Problem 4)
The golf scores for the 20 members of a country club were as follows:
81, 76, 107, 95, 119, 92, 83, 74, 108, 88
95, 74, 83, 76, 97, 82, 79, 91, 93, 89
Create a relative frequency histogram using ten-point class widths to show the
distribution of the scores.
Problem 6)
Black Hole Pizza Parlor instructs its cooks to put a "handful" of cheese on each large
pizza. A random sample of six such handfuls were weighed. The weights to the nearest
ounce were:
3
2
3
4
3
5
a) Find the mode, the median and the mean weight of the handfuls of cheese.
b) Find the range and the stand deviation of the weights
The mode is 3
The median is 3
The mean is 3.333
The range is 5-2=3
The standard deviation is calculated as follows:
1/5 * ( (2-3.33)^2 + (3-3.33)^2 +(3-3.33)^2 +(3-3.33)^2 +(4-3.33)^2 +(5-3.33)^2 ) =
1.0328
Problem 8)
In a random sample of eight military contracts involving cost overruns, the following
information was obtained. x = big price of the contract (in millions of dollars) and y =
cost of overrun (expressed as a percent of the bid price).
x
y
6 10 3 5 9 18 16 21
31 25 39 35 29 12 17 8
a) Draw the scatter diagram for this data.
b) Find the slope, b, and the intercept, a, for the least-squares line. Write the
equation of the least-squares line.
Slope = -1.68
y-intercept = 43.0
regression equation: y = 43.0 - 1.68 x.
c) Graph the least-squares line on your scatter diagram.
d) If an overrun contract was bid at 12 million dollars, what does the leastsquares line predict for the cost of overrun (as a percent of bid price)?
22.819%
Problem 9)
Mary Sue wants to know if there is a connection between attendance at craft fairs and the
number of exhibitors who have booths at the fair. For a random sample of seven local
craft fairs, she chose a random day of the fair and recorded the number of exhibitors. In
the data below, x represents the number of exhibitors and y represents the attendance in
hundreds of people.
x 35 55 75 95 100 135 150
y 1.2 2.1 4.2 5.4 5.8 6.2 9.5
a) Draw the scatter diagram for the data.
b) Calculate the sample correlation coefficient, r.
r=0.9618. This is the square root of r^2 found in part b.
c) Calculate the coefficient of determination, r2.
From the regression output, SSR/SST = r^2 = 42.48/45.93 = 0.925
d) What does the coefficient of determination tell you about the variation in
attendance and the variation in the number of exhibitors?
It tells us that 92.5% of the variability in the number of attenders can be explained by
using the number of exhibitors as a predictor variable.
Problem 12)
Evaluate:
a) P6,4 = 360
b) C7,2 = 21
c) P4,4 = 24
d) C9,0 = 1
Problem 15)
Richard has just been given a ten-question multiple choice test in his history class. Each
question has five answers only one of which is correct. Since Richard has not attended
class recently, he does not know any of the answers. Assume that Richard guesses
randomly on all ten questions.
P=0.2, n=10. Number right follows a binomial distribution.
a) Find the probability that he will answer all 10 questions correctly.
P(x=10) = 0.000000102 (from excel using =binomdist(10,10,.2,0)
b) Find the probability that he will answer 5 or more questions correctly.
=P(x>=5) = 1-P(x<=4) = 0.0328 from excel using =1-binomdist(4,10,.2,1)
c) Find the probability that he will answer none of the questions correctly.
=P(x=0) = 0.1074 (from excel, using =binomdist(0,10,.2,0)
d) Find the probability that he will answer at least 3 questions correctly.
=P(x>=3) = 1-P(x<=2) = 0.3222 (from excel using =binomdist(2,10,.2,1)
Problem 16)
Long-term history has shown that 65% of all elected offices in a rural county have been
won by Republican candidates. This year there are 5 offices up for public election in the
county Let r be the number of public offices won by Republicans.
a) Find P(r) for r=0,1,2,3,4, and 5
P(x=0)=0.005252188
P(x=1)=0.048770313
P(x=2)=0.181146875
P(x=3)=0.336415625
P(x=4)=0.312385938
P(x=5)=0.116029063
b) Make a histogram for the r probability distribution.
c) What is the expected number of Republicans who will win office in the
coming election?
E(X) = np = 5*0.65 = 3.25
d) What is the standard deviation of r?
sqrt(npq) = 1.067
Problem 18)
Let x be a random variable that represents the length of time it takes a student to write a
term paper for Dr. Adam's Sociology class. After interviewing many students, it was
found that x has an approximately normal distribution with mean μ = 6.8 hours and
standard deviation σ = 2.1 hours.
Convert each of the following x intervals to standardized z intervals:
a) x ≤ 7.5  z<=0.333
b) 5 ≤ x ≤ 8 00 -0.857142857 <= z <= 0.571428571
c) x ≥ 4  z>=-1.333
Convert each of the following z intervals to raw score x intervals:
d) z ≥ -2  x>=2.6
e) 0 ≤ z ≤ 2  6.8<= x<=11
f) z ≤ 3  x<=13.1
Problem 19)
Researchers at a pharmaceutical company have found that the effective time duration of a
safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard
deviation 0.3 hour. For a patient selected at random:
a) What is the probability that the drug will be effective for 2 hours or less?
P(x<2) = P(z<0) = 0.5
b) What is the probability that the drug will be effective for 1 hour or less?
P(x<1) = P(z<(1-2)/0.3) = P(z<-3.333) = 0.0004
c) What is the probability that the drug will be effective for 3 hours or more?
P(x>3) = P(x<1) = 0.0004
Problem 20)
Roger has read a report that the weights of adult mail Siberian tigers have a distribution
which is approximately normal with mean μ = 390 lb and σ = 65 lb.
a) Find the probability that an individual male Siberian tiger will weigh more
than 450 lb.
P(x>450) = P(z>(450-390)/65) = P(z>0.923) = 0.178
b Find the probability that a random sample of 4 male Siberian tigers will have a
sample mean weight more than 450 lb.
P(x-bar>450) = P(z>(450-390)/(65/sqrt(4)) = P(z>1.846) = 0.032