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) 13) (A) (B) (C) (D) (E)
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 80% of employees listen to music. Of those who listen to music, only 10% smoke. What fraction of employees do both of these things (smoking and listening to music) during a typical workday?
A) .16 B) .08 C) .95 D) .1125 E) None of the Above.
2) A single die is thrown once. A={1,2,4}, B={3,4,5}. 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) 4.71
B) 22.22
C) 5
D) 4.52
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) 1.41 B) 2 C) 1 D) 4 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 larger 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 and , with probabilities p() and p(). If E[X]=0, = –3 and p()=.75, then what is the Z-score corresponding to?
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 negative?
A) .8413 B) .3370 C) .4045 D) .6630 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) 0 B) .0188 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 standard error of the sample mean must be zero.
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 sampling distribution of the sample mean is the same as the distribution of the population.
E) None of the above.