This Is the Answer Sheet. Circle the Choice Which Best Answers Each Question on the Exam

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!

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)

COR1-GB.1305.03

MIDTERM

1)  On Radio Airplay, you pay to play your song to listeners. Each play costs you 3 cents. A certain proportion p of listeners who hear your song will buy it on iTunes (who will pay you 70 cents per song purchased). What value of p would result in an expected profit of zero?

A) .9571 B) .2570 C) .0571 D) .0429 E) None of the Above

2)  In sampling from a given population, as the sample size is increased, the standard error

A) Tends to the population standard deviation, σ B) Approaches infinity C) Approaches zero

3)  Suppose that 23% of likely voters in Wyoming support Hillary Clinton for president. Tomorrow, you are going to select a random sample of three likely voters in Wyoming. What is the probability that exactly two of them support Clinton? (Give an exact answer)

A) .2444 B) .1344 C) .1222 D) .8656 E) None of the Above

4)  Suppose that the number of supernovas observed next year is normally distributed, with the mean equaling three times the standard deviation. Suppose also that the probability of at least one supernova being observed next year is .1587. What is the expected number of supernovas observed next year?

A) .25 B) .75 C) 1 D) 1.5 E) None of the Above

5)  If Adele releases an album next year, then there is a 60% chance that she will go on tour next year. Based on recent data, the probability that Adele will release an album next year is 30%. What is the probability that, next year, Adele will release an album but not go on tour?

A) .12 B) .18 C) .4 D) .88 E) None of the Above.

6)  What is the probability that a standard normal random variable is greater than −.35?

A) .1368 B) .6368 C) .3632 D) .8632 E) None of the Above.

7)  If X is normal with mean 3 and standard deviation 2, what is the probability that X is less than 5?

A) 1 B) .1587 C) .6587 D) .8413 E) None of the Above

8)  Which of the following formulas implies that the sample mean is unbiased?

A) B) C) D) E) None of the Above

9)  If X is binomial with n=5 and p=.32, then what is the probability that X will equal 2?

A) .3482 B) .3277 C) .6963 D) .6723 E) None of the Above

10) If X is a random variable taking the value 1 with probability .2 and −3 with probability .8, what is the standard deviation of X?

A) −2.2 B) 6.34 C) 2.56 D) 1.6 E) None of the Above

11) You are going to throw two dice once. Let A = {Total is 11} and let B = {Total is at least 10}. Then A, B are

A) Independent B) Mutually Exclusive C) Neither independent nor mutually exclusive

12) Suppose that annual incomes of employed residents in a certain county have a mean of $130000 and a standard deviation of $40000. If you take a random sample of 25 employed residents in the county, what is the probability that their average income falls between $130000 and $140000?

A) .4013 B) .0987 C) .1056 D) .3944 E) None of the Above

13) If X is binomial with n=4 and p=1/3, then the z-score corresponding to the value x=1 is:

A) −.3536 B) 1.333 C) −.9428 D) .6666 E) None of the Above.

14) In random sampling from an infinite population, if we quadruple the sample size, then the ratio of the new standard error to the original one is:

A) 4 B) 1/4 C) 2 D) 1/2 E) None of the Above

15) For a data set of size n=2, the sample mean is zero and the sample standard deviation is. What is the z-score corresponding to the smallest data point?

A) .7071 B) −.7071 C) −.2496 D) −.3010 E) None of the Above