Download Midterm, Version 1

B01.1305.03
MIDTERM
Name:________________________
This is the answer sheet. Circle the choice which best answers each question on
the exam. Do not write anything else on this sheet (besides your name and the
circles). When you are finished, hand in just this answer sheet. You can keep the
question sheets. There are 15 questions, each worth 5 points. Everyone receives
25 points for free. Good Luck!
1) (A) (B) (C) (D) (E)
11) (A) (B) (C) (D) (E)
2) (A) (B) (C) (D) (E)
12) (A) (B) (C) (D) (E)
3) (A) (B) (C) (D) (E)
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4) (A) (B) (C) (D) (E)
14) (A) (B) (C) (D) (E)
5) (A) (B) (C) (D) (E)
15) (A) (B) (C) (D) (E)
6) (A) (B) (C) (D) (E)
7) (A) (B) (C) (D) (E)
8) (A) (B) (C) (D) (E)
9) (A) (B) (C) (D) (E)
10) (A) (B) (C) (D) (E)
B01.1305.03
MIDTERM
1) Suppose that in a certain office during a typical workday, 20% of employees
smoke, and 75% of employees listen to music. Of those who listen to music,
only 15% smoke. What fraction of employees do both of these things
(smoking and listening to music) during a typical workday?
A) .15 B) .8 C) .95 D) .1125 E) None of the Above.
2) A single die is thrown once. A={1,2,4}, B={2,4,5}. Then P(B|A)=
A) 1/2 B) 2/3 C) 1/4 D) 1/3 E) None of the Above.
3) If a single die is thrown once, A={A six is thrown}, B={An even number is
thrown}, then A,B are
A) Mutually Exclusive B) Independent C) Dependent
D) Complementary events E) None of the Above
4) The profit from an investment will be zero with probability .4, negative 1
million Dollars with probability .1, positive 1 million Dollars with probability
.5. The expected profit for this investment is:
A) Zero
B) .4 Million
C) –.4 Million
D) .6 Million
E) None of the above.
5) If we toss a single die 100 times independently, and X is the number of times
that the value thrown is at most two, then what is the standard deviation of X?
A) 4.52
B) 22.22
C) 5
D) 4.71
E) None of the above.
6) If X is normal with mean 3 and standard deviation 2, then what is Prob(X>5)?
A) 0
B) .1587
C) .8413
D) .3413
E) None of the Above.
7) If X is normal with mean zero and P(X< –4)=.0228, then what is the standard
deviation of X?
A) 4 B) 1 C) 2 D) 1.41 E) None of the Above.
8) If P(A)>0, P(B)>0 and P(B|A)=0, then A,B must be
A) Independent B) Dependent
C) Complementary Events D) None of the Above
9) Take a fair coin. Label Heads as 1. Label Tails as 0. Toss the coin twice,
independently. What is the expected value of the smaller of the two numbers
that are tossed?
A) 1 B) 1/4 C) 1/2 D) 3/4 E) None of the Above
10) The Central Limit Theorem says that if we take a random sample of size n
from an infinite population, then if n is sufficiently large
A) The distribution of the values in the sample will be approximately normal
B) The standard error of the sample mean will approach the standard
deviation of the population.
C) The distribution of the sample mean will be approximately normal.
D) The bias of the sample mean will get smaller
E) None of the above.
11) Suppose that X is a discrete random variable, taking on one of two possible
values x1 and x 2 , with probabilities p( x1 ) and p( x 2 ). If E[X]=0, x1 =3 and
p( x1 )=.75, then what is the Z-score corresponding to x 2 ?
A) .25 B) –1.73 C) 1.73 D) –9 E) None of the Above.
12) If X Y and Z are independent with mean 1 and standard deviation 1,
what is the probability that exactly one of these random variables is positive?
A) .8413 B) .9960 C) .0636 D) .1587 E) None of the above.
13) An electronics store has 500 iPhones in stock. Each customer who enters the
store can buy as many iPhones as they want, while supplies last. Based on their
market research, the store knows that the distribution of the number of iPhones
desired by a customer has a mean of 0.85 and a standard deviation of 0.6. If 625
customers enter the store today, what is the probability that they will all be able to
purchase the iPhones they desire?
A) .0188 B) 0 C) 1 D) .4681 E) None of the Above.
14) If X is standard normal and Y= –X, then P(X>2 and Y< –2) is:
A) .0005 B) .0228 C) .0456 D) .4772 E) None of the Above
15) If the sample size is 1, then
A) The sampling distribution of the sample mean is the same as the
distribution of the population.
B) The sampling distribution of the sample mean must be normal.
C) The standard error of the sample mean is less than the standard deviation of
the population.
D) The standard error of the sample mean must be zero.
E) None of the above.