Question 1

Let $$Z be $$the standard normal random variable. What is the mean of $$Z$$?

Accepted Answer

$$0$$

Question 2

Which of the following statements about probability is INCORRECT?

Accepted Answer

$$\Pr(X \u003e a) = 1 - a$$

Question 3

Suppose you roll two fair 8-sided dice. What is the probability that the sum of the dice is 16?

Accepted Answer

$$\dfrac{3}{64}$$

Question 4

A company has 15% left-handed employees and 6% left-handed males. If half the employees are male, what is the probability that a randomly selected employee is either male or left-handed (or both)?

Accepted Answer

$$0.59$$

Question 5

How many different Virginia license plates are possible if each plate has four letters followed by three digits, and any letter or digit can be used?

Accepted Answer

$$26^4$$ 	imes $$10^3$$

Question 6

A blood bank recorded 28 donors with type O, Rh-negative blood out of 409 total donors. What is the probability that a randomly selected donor has type O and is Rh-negative?

Accepted Answer

$$\dfrac{28}{409}$$

Question 7

A card is drawn from a standard deck. What is the probability that the card is between 4 and 6 (inclusive), or is a club?

Accepted Answer

$$\dfrac{16}{52}$$

Question 8

Suppose the mean existing home sales price is $$296,700 with a standard deviation of 50$$,000. For a random sample of 12 homes, what is the probability that the mean sales price is more than $$275,000$$? (Assume normality.)

Accepted Answer

$$0.9977$$

Question 9

Which of the following is NOT a legitimate probability distribution for a discrete random variable $$X$$?

Accepted Answer

If $$\sum_k \Pr(X=k) = 1.2$$

Question 10

A restaurant offers 6 appetizers, 12 entrees, and 8 desserts. How many different meals are possible if you choose one of each?

Accepted Answer

$$576$$

Question 11

Let $$U be a $$uniform random variable on the interval $$[1,5]. $$What is $$\Pr(1.25 \u003c U \u003c 3.5)$$?

Accepted Answer

$$0.5625$$

Question 12

Suppose $$X \sim N(41, 12^2$). $$What is the probability $$\Pr(20 \u003c X \u003c 50)$$?

Accepted Answer

$$0.7977$$

Question 13

In a group of U.S. adults, total cholesterol is normally distributed with mean $$190 mg/dL $$and standard deviation $$40.9 mg/dL. $$What is the highest cholesterol level to still be in the bottom 1%?

Accepted Answer

$$190 + (-2.33) 	imes 40.9$$

Question 14

A roulette wheel has 2 green, 18 red, and 18 black spaces. If the wheel is spun 3 times, what is the probability that none of the spins are red?

Accepted Answer

$$\left(\dfrac{20}{38}\$$right)^3$$

Question 15

Let $$Y be a $$discrete random variable with values $$-1, 1, 2$$ and probabilities $$0.2, 0.5, 0.3$$ respectively. What is the expected value $$E(Y)$$?

Accepted Answer

$$0.9$$

Question 16

Suppose you flip a coin and then roll a 4-sided die. How many elements are in the sample space?

Accepted Answer

$$8$$

Question 17

Which of the following pairs of events are mutually exclusive?

Accepted Answer

Selecting a chemistry major and selecting a physics major (non-double major students)

Question 18

In Poker, what is the probability of being dealt a 5-card hand containing $$A$$, $$K$$, $$Q$$, $$J$$, $$10$$ all of the same suit?

Accepted Answer

$$\dfrac{4}{2,598,960}$$

Question 19

Suppose the mean annual salary for chauffeurs is $$30,800$$ with $$\sigma = 5,600. $$For a random sample of $$45$$ chauffeurs, what is the probability that the sample mean is more than $$30,000$$?

Accepted Answer

$$0.9878$$

Question 20

Using the standard normal table, what is $$\Pr(Z  1.68)$$?

Accepted Answer

$$0.9539$$

Step-by-Step Guidance for Math 111 Exam 2 Practice (Statistics)

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