Question 1

Which of the following is a requirement for a probability distribution?

Accepted Answer

The random variable x must be numerical and each value must be associated with a probability.

Question 2

Given the probability distribution for the number of females in two births: $$x = 0, 1, 2$$ with $$P(x) = 0.25, 0.50, 0.25$$ respectively, what is the mean number of females?

Accepted Answer

$$\mu = 1.0$$

Question 3

Which formula correctly calculates the variance $$\$$sigma^2$$ for a discrete probability distribution?

Accepted Answer

$$\$$sigma^2$$ = \sum (x - \mu)^2$ \cdot P(x)$$

Question 4

A probability histogram differs from a relative frequency histogram in that:

Accepted Answer

It uses probabilities instead of relative frequencies on the vertical axis.

Question 5

Which of the following is NOT a requirement for a binomial probability distribution?

Accepted Answer

The trials must be dependent on each other.

Question 6

A survey finds that 5% of adults are cashless. If 10 adults are randomly selected, what is the probability that exactly 2 are cashless? (Use the binomial formula.)

Accepted Answer

$$P(2) = \dfrac{10!}{8!2!} (0.05)^2$ (0.95)^8$

Question 7

For a binomial distribution with $$n = 460$$, $$p = 0.5$$, and $$q = 0.5$$, what is the mean and standard deviation?

Accepted Answer

$$\mu = 230,\ \sigma = 10.7$$

Question 8

Which of the following scenarios is best modeled by a Poisson distribution?

Accepted Answer

The number of patients arriving at an ER in one hour.

Question 9

If the mean number of hurricanes per year is $$\mu = 5.5$$, what is the probability of exactly 6 hurricanes in a year according to the Poisson formula?

Accepted Answer

$$P(6) = \dfrac{5.5^6$ e$$^{-5.5}$$}{6!}$$

Question 10

A continuous random variable has a uniform distribution between 0 and 5. What is the probability that a randomly selected value is at least 2?

Accepted Answer

$$P(x \geq 2) = 0.6$$

Question 11

Which formula is used to convert a value $$x$$ from a normal distribution with mean $$\mu$$ and standard deviation $$\sigma to a $$standard normal $$z$$ score?

Accepted Answer

$$z = \dfrac{x - \mu}{\sigma}$$

Question 12

If the area to the left of $$z = 1.27$$ under the standard normal curve is 0.8980, what is the probability that a randomly selected value is less than 1.27?

Accepted Answer

0.8980

Question 13

A sample of 950 students found that 53% take online courses. What is the best point estimate of the population proportion?

Accepted Answer

0.53

Question 14

Which of the following is the correct formula for the margin of error $$E$$ for a confidence interval for a population proportion?

Accepted Answer

$$E = z_{\alpha/2} \sqrt{\dfrac{\hat{p}\hat{q}}{n}}$$

Question 15

If a 95% confidence interval for a population proportion is (0.405, 0.455), what is the correct interpretation?

Accepted Answer

We are 95% confident that the interval from 0.405 to 0.455 actually does contain the true value of the population proportion.

Question 16

Which method should be used to construct a confidence interval for a population mean when the population standard deviation $$\sigma is $$unknown and the sample size is less than 30?

Accepted Answer

Use the Student t distribution.

Question 17

What is the formula for the margin of error $$E$$ when constructing a confidence interval for a population mean with unknown $$\sigma$$?

Accepted Answer

$$E = t_{\alpha/2} \dfrac{s}{\sqrt{n}}$$

Question 18

Which of the following statistics is an unbiased estimator of its corresponding population parameter?

Accepted Answer

Sample mean $$\bar{x}$$

Question 19

According to the Central Limit Theorem, for all samples of size $$n \u003e 30$$, the sampling distribution of $$\bar{x}$$ can be approximated by a normal distribution with mean $$\mu$$ and standard deviation:

Accepted Answer

$$\dfrac{\sigma}{\sqrt{n}}$$

Probability Distributions and Estimation in Elementary Statistics

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