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COR1-GB.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!
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COR1-GB.1305.03
MIDTERM
1) The number of peanut M&Ms in a 1.74 ounce bag has a mean of 12 and a
standard deviation of 1. If you buy 10 bags (selected at random) and open
them, what is the probability that the total number of M&Ms is at least 125?
A) .6915 B) .9429 C) .0571 D) .3085 E) None of the Above
2) Suppose that the high temperature at New York’s Central Park for January 1
is normally distributed with a mean of 35 degrees (Fahrenheit) and a standard
deviation of 9 degrees. What is the probability that on next January 1 the high
temperature there will exceed 50 degrees?
A) .4525 B) .9525 C) .5475 D) .0475 E) None of the Above
3) What is the probability that a standard normal random variable will be
between −1.5 and 1.6?
A) .8784 B) .0120 C) .4452 D) .5548 E) None of the Above
4) Suppose A, B are two events with P(A)>0 and P(B)>0. Then the probability
that A and B will both happen
A) Must be less than P(A) B) May be equal to P(A).
5) What is the probability that a normal random variable with mean 1 and
standard deviation 2 will be between −1 and 3?
A) .8400 B) .6826 C) .1600 D) .3413 E) None of the Above
6) Suppose there is an 80% probability that the Fed will raise interest rates in
2016. Suppose also that there is a 60% probability that if the Fed raises
interest rates in 2016, the Dow return for 2016 will be negative. What is the
probability that the Fed will raise interest rates in 2016 and the Dow return for
2016 will be negative?
A) .6 B) .48 C) .8 D) .52 E) None of the Above
7) Two dice are thrown, independently, one after the other. Let A={First die is
4}, B={Sum of the two dice is 7}. Then A, B are
A) Independent B) Mutually Exclusive C) Dependent but not Mutually
Exclusive D) None of the Above.
8) If the population standard deviation is 1, then the standard error of the mean
will be less than or equal to .01 whenever the sample size n is:
A) Less than 100 B) Greater than or equal to 100 C) Less than 10000 D)
Greater than or equal to 10000 E) None of the Above.
9) You are going to poll a random sample of 2000 managers employed in the
U.S. and ask them if they like their job. The margin of error is:
A) .0002 B) .0438 C) .0112 D) .0219 E) None of the Above
10) Suppose that 50 people, selected at random from some demographic group,
are asked to watch a particular video on YouTube. If the probability that a
particular person from this group “likes” the video is .015 (the same
probability for everyone in the group), then what is the probability that exactly
two of the 50 people will “like” the video?
A) .1334 B) .0120 C) .9880 D) .1526 E) None of the Above
11) If A, B are independent events with P(A)=.4 and P(AB)=.7 then P(B) is:
A) .3 B) .5 C) .28 D) .7 E) None of the Above.
12) Suppose that X is a binomial random variable with n=20 and p=.7. We obtain
one observation of X, and the observed value is 17. The z-score corresponding
to this observed value is:
A) .7143 B) 1.464 C) 3 D) −1.464 E) None of the Above
13) Suppose that X is a discrete random variable that can take on one of the two
values, 1 and 3, with equal probabilities. What is the standard deviation of X?
A) 1.41 B) 1 C) 2 D) 1.64 E) None of the Above.
14) Suppose that scores on a certain standardized test are normally distributed
with a mean of 1125 and a standard deviation of 150. At what percentile is a
score of 1320 on this exam?
A) 40.32 B) 99.87 C) 97.72 D) 90.32 E) None of the Above
15) You will throw a fair die 10 times. What is the standard deviation of the
number of times you will throw a 3?
A) .5 B) 1.389 C) 1.179 D) 0.1179 E) None of the Above