Question 1

Which of the following best describes a discrete random variable?

Accepted Answer

A variable whose possible values are countable and distinct.

Question 2

A probability distribution is valid if:

Accepted Answer

The sum of all probabilities equals 1.

Question 3

Given a discrete probability distribution with $$P(X=1)=0.2$$, $$P(X=2)=0.5$$, $$P(X=3)=0.3$$, what is the expected value $$E(X)$$?

Accepted Answer

$$E(X) = 2.1$$

Question 4

Which scenario below is NOT a binomial experiment?

Accepted Answer

Measuring the heights of 20 students.

Question 5

A fair coin is flipped 4 times. What is the probability of getting exactly 2 heads? Use the binomial formula: $$P(X=k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$.

Accepted Answer

$$0.375$$

Question 6

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

Accepted Answer

$$z = 1.5$$

Question 7

A hospital records the weights of newborns, which are normally distributed with $$\mu = 3.5 kg $$and $$\sigma = 0.5 kg. $$What is the probability that a randomly selected newborn weighs less than $$3.0 kg$$? (Use the standard normal table.)

Accepted Answer

$$P \approx 0.1587$$

Question 8

If the area to the left of a $$z-$$score is $$0.975$$, what is the corresponding $$z-$$score?

Accepted Answer

$$z \approx 1.96$$

Question 9

A sample of 36 students has a mean score of 80. If the population standard deviation is $$\sigma = 12$$, what is the margin of error for a 95% confidence interval? (Use $$z_{\alpha/2} = 1.96)$$

Accepted Answer

$$M = 3.92$$

Question 10

According to the Central Limit Theorem, as sample size increases:

Accepted Answer

The sampling distribution of the sample mean approaches a normal distribution.

Question 11

A confidence interval for a population mean (sigma unknown) is constructed using which distribution?

Accepted Answer

t-distribution

Question 12

If you want to estimate a population proportion with a margin of error $$E = 0.03$$ and confidence level 95% ($$z_{\alpha/2} = 1.96$$), what is the minimum sample size required? (Assume $$\hat{p} = 0.5)$$

Accepted Answer

$$n = 1068$$

Question 13

A researcher wants to construct a 99% confidence interval for the mean cholesterol level in adults. Which $$z-$$value should be used?

Accepted Answer

$$z = 2.576$$

Question 14

Which formula is used to find the margin of error for a population mean when $$\sigma is $$known?

Accepted Answer

$$E = z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$$

Question 15

A random sample of 50 patients shows 18 have a certain disease. What is the point estimate for the population proportion?

Accepted Answer

$$\hat{p} = 0.36$$

Question 16

Which of the following is NOT a requirement for constructing a confidence interval for a population proportion?

Accepted Answer

The population must be normally distributed.

Question 17

A manufacturer tests 100 batteries and finds 8 are defective. Construct a 90% confidence interval for the proportion of defective batteries. ($$z_{\alpha/2} = 1.645)$$

Accepted Answer

$$0.08 \pm 0.025$$

Question 18

If the mean of a discrete probability distribution is $$\mu = 4$$ and the variance is $$\$$sigma^2$$ = 9$$, what is the standard deviation?

Accepted Answer

$$\sigma = 3$$

Question 19

A sample of 25 students has a mean test score of 70 and a sample standard deviation $$s = 8. $$What is the 95% confidence interval for the mean? (Use $$t_{\alpha/2} = 2.064)$$

Accepted Answer

$$70 \pm 3.3$$

Question 20

Which calculator function would you use to find the probability of getting at least 3 successes in a binomial experiment with $$n = 10$$ and $$p = 0.2$$?

Accepted Answer

binomcdf(10, 0.2, 2)

Study Guide: Probability Distributions, Normal Distributions, and Confidence Intervals (Chapters 4-6)

Study Guide - Practice Questions

Study Guide - Flashcards