Midterm 1 Practice
1. What are the mean and the standard deviation of the following sample data: -3; -1;
2; 4; 8?
2. A student was given the following sample of (x,y) data: (3;-2); (0;0); (-1;2). The task
was to …nd the sample correlation coe¢ cient. The student correctly computed the mean
and the standard deviation of y as y = 0 and sy = 2. However, the student made a mistake
computing the mean and the standard deviation of x as x = 2 and sx = 1. Afterwards, the
student used the correct procedure to compute the sample correlation coe¢ cient. What is
the answer the student got? (Basically, you need to compute the correlation using given
values of mean and standard deviation of x instead of the correct ones).
3. An urn contains 3 red balls and 7 green balls. What is the probability of getting
exactly 2 red balls in a sample of size 4 (sampling is done without replacement)? The
answer should be a number.
4. An inspector examines items coming from an assembly line. A review of his record
reveals that he accepts only 8% of all defective items. It was also found that 1% of all
items from the assembly line are both defective and accepted by the inspector. What is
the probability that a randomly chosen item from this assembly line is defective?
5. A publisher sends advertising materials for an accounting text to 80% of all professors
teaching the appropriate accounting course. Thirty percent of the professors who received
this material adopted the book, as did 10% of the professors who did not receive the
material. What is the probability that a professor who adopts the book has received the
advertising material?
6. A data sample contains all integers from
531. What is the mean of this sample?
530 to
380 and all integers from 379 to
7. Your dataset contains three observations on x and y. You know the …rst two (x; y)
points: (239; 120) and (240; 115). You know only the x-value of the third point. It is 245.
What is the y-value of that point if the correlation between x and y is -1?
8. We will de…ne an outlier as a value which is more than 1.5 times the interquartile
range below the …rst quartile (Q1 ) or more than 1.5 times the interquartile range above the
third quartile (Q3 ). Identify all outliers in the following sample:
15; 18; 23; 80; 82; 88; 97; 100; 103; 108; 112; 120; 150; 178; 181
9. There are two dice. One is standard and the other only has three …ves and three
sixes. One die was randomly chosen and rolled twice. What is the probability that it was
the second die (with three …ves and three sixes) that was rolled if
a) numbers 3 and 5 came up (the order is unknown)?
b) numbers 5 and 6 came up (the order is unknown)?
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