Question 1

Which of the following best describes the difference between a discrete and a continuous probability distribution?

Accepted Answer

A discrete probability distribution is used for variables that are counted (e.g., number of students), while a continuous probability distribution is used for variables that are measured and can take any value within an interval (e.g., weight).

Question 2

Which of the following is NOT a requirement for a binomial experiment?

Accepted Answer

Each trial can have more than two possible outcomes.

Question 3

Suppose a random variable $$X$$ has the following probability distribution: $$P(X=1)=0.2$$, $$P(X=2)=0.5$$, $$P(X=3)=0.3. $$What is the mean (expected value) of $$X$$?

Accepted Answer

$$\mu = (1)(0.2) + (2)(0.5) + (3)(0.3) = 2.1$$

Question 4

A company finds that 84% of its customers are satisfied. If 5 customers are surveyed, what is the probability that exactly 4 will be satisfied? (Use the binomial formula.)

Accepted Answer

$$P(4,5) = \frac{5!}{(5-4)!4!}(0.84)^4$(0.16)^1 = 0.3983$

Question 5

Which formula gives the standard deviation of a binomial distribution with $$n$$ trials and probability of success $$p$$?

Accepted Answer

$$\sigma = \sqrt{npq}$$, where $$q = 1-p$$

Question 6

A normal distribution has mean $$\mu = 45$$ and standard deviation $$\sigma = 5. $$What is the $$z-$$score for $$x = 48$$?

Accepted Answer

$$z = \frac{48 - 45}{5} = 0.6$$

Question 7

Which of the following statements about the normal distribution is FALSE?

Accepted Answer

The probability of any single exact value is greater than zero.

Question 8

If the population mean is $$\mu = 100$$ and the population standard deviation is $$\sigma = 20$$, what is the standard error of the mean for samples of size $$n = 25$$?

Accepted Answer

$$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{20}{5} = 4$$

Question 9

A sample of 40 health club members has a mean age of 36.1 years. The population mean is claimed to be 37 years with a standard deviation of 5 years. What is the $$z-$$score for the sample mean?

Accepted Answer

$$z = \frac{36.1 - 37}{5/\sqrt{40}} = \frac{-0.9}{0.7906} = -1.14$$

Question 10

Which of the following is a correct application of the Central Limit Theorem?

Accepted Answer

For any population, the distribution of sample means will be approximately normal if the sample size is large enough ($$n \geq 30$$), regardless of the population's shape.

Question 11

A political party claims 60% support. In a sample of 250, 130 support the party. What is the $$z-$$score for the sample proportion?

Accepted Answer

$$z = \frac{0.52 - 0.6}{\sqrt{0.6 	imes 0.4 / 250}} = \frac{-0.08}{0.0310} = -2.58$$

Question 12

Which Excel function would you use to find the probability of exactly $$x$$ successes in a binomial experiment?

Accepted Answer

=BINOM.DIST(x, n, p, FALSE)

Question 13

If a normal distribution has $$\mu = 790$$ and $$\sigma = 160$$, what is the probability that a randomly selected value is less than $$700$$?

Accepted Answer

First, calculate $$z = \frac{700 - 790}{160} = -0.56. $$Then, $$P(X \u003c 700) = P(Z \u003c -0.56) = 0.2877$$

Question 14

Which of the following is a property of the standard normal distribution?

Accepted Answer

It has a mean of 0 and a standard deviation of 1.

Question 15

A survey finds that 10% of golfers are left-handed. In a sample of 200, what is the probability that more than 12% are left-handed?

Accepted Answer

Calculate $$\sigma_p = \sqrt{0.1 	imes 0.9 / 200} = 0.0212$$, $$z = \frac{0.12 - 0.1}{0.0212} = 0.94$$, so $$P(p \u003e 0.12) = 1 - 0.8264 = 0.1736$$

Question 16

Which of the following is a correct interpretation of the expected monetary value (EMV) in a business context?

Accepted Answer

EMV represents the long-term average outcome in dollars if the same decision or investment is made repeatedly under the same probability distribution.

Probability Distributions and Sampling Distributions in Business Statistics

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