Question 1

Which of the following is NOT a property of a continuous probability distribution?

Accepted Answer

The random variable is discrete.

Question 2

Suppose the waiting time at a coffee shop is uniformly distributed between 0 and 10 minutes. What is the probability that a randomly selected customer waits more than 7 minutes?

Accepted Answer

$$P(X \u003e 7) = 0.3$$

Question 3

Given a normal distribution with mean $$\mu = 50$$ and standard deviation $$\sigma = 10$$, what is the $$z-$$score for $$x = 65$$?

Accepted Answer

$$z = 2$$

Question 4

A variable $$X is $$normally distributed with $$\mu = 100$$ and $$\sigma = 15. $$What is the probability that $$X is $$less than 115?

Accepted Answer

$$P(X \u003c 115) = 0.841$$

Question 5

The area under the curve in a probability density function between two points $$a$$ and $$b$$ represents:

Accepted Answer

The probability that the random variable falls between $$a$$ and $$b.$$

Question 6

If the mean SAT score is 1511 with a standard deviation of 312, what is the probability that a randomly selected student scores higher than 1600?

Accepted Answer

$$P(X \u003e 1600) = 0.388$$

Question 7

Which formula gives the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

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

Question 8

A sample of 36 students has an average SAT score of 1600. If the population mean is 1511 and the population standard deviation is 312, what is the $$z-$$score for this sample mean?

Accepted Answer

$$z = \frac{1600 - 1511}{52} = 1.71$$

Question 9

If the population is not normally distributed and the sample size $$n \leq 30$$, which of the following is true about the sampling distribution of the sample mean?

Accepted Answer

It cannot be well approximated by a normal distribution.

Question 10

The critical value $$z_{0.05}$$ for the standard normal distribution is:

Accepted Answer

$$z_{0.05} = 1.645$$

Question 11

A sample proportion $$\hat{p} is $$calculated from a sample of size $$n = 100$$ with $$p = 0.4. $$What is the standard deviation of the sampling distribution of $$\hat{p}$$?

Accepted Answer

$$\sigma_{\hat{p}} = \sqrt{\frac{0.4(1-0.4)}{100}} = 0.049$$

Question 12

If $$P(Z \u003c z) = 0.8461$$ for a standard normal variable, what is the value of $$z$$?

Accepted Answer

$$z = 1.02$$

Question 13

The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean:

Accepted Answer

Approaches a normal distribution, regardless of the population's distribution.

Question 14

A water taxi is rated for a load limit of 3500 lb and 25 passengers. If the mean weight of men is 182.9 lb with a standard deviation of 40.8 lb, what is the probability that the average weight of 25 randomly selected men exceeds 140 lb?

Accepted Answer

$$P(\bar{X} \u003e 140) = 1$$

Question 15

If the area to the left of $$z is 0.2033$$, what is the value of $$z$$?

Accepted Answer

$$z = -0.83$$

Question 16

The 95th percentile of the standard normal distribution corresponds to which $$z-$$score?

Accepted Answer

$$z = 1.645$$

Question 17

If the weights of three-year-olds are normally distributed with $$\mu = 30.7$$ pounds and $$\sigma = 3.6$$ pounds, what is the probability that a randomly selected child weighs at least 30 pounds?

Accepted Answer

$$P(X \geq 30) = 0.577$$

Question 18

Which of the following best describes a density curve?

Accepted Answer

A smooth curve that represents the distribution of a continuous variable.

Question 19

If $$P(-z \u003c Z \u003c z) = 0.80$$ for a standard normal variable, what is the value of $$z$$?

Accepted Answer

$$z = 1.28$$

Normal Probability Distributions and the Central Limit Theorem

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