Q: Suppose the waiting time for a bus is uniformly distributed between 0 and 10 minutes. What is the probability that a person waits more than 7 minutes?

$$P(\text{wait} \u003e 7) = (10 - 7) \times 0.10 = 0.30$$

Question 1

Which of the following statements best describes the relationship between probability and area under a density curve for a continuous random variable?

Accepted Answer

Probability is equal to the area under the density curve between two values.

Question 2

Suppose the waiting time for a bus is uniformly distributed between 0 and 10 minutes. What is the probability that a person waits more than 7 minutes?

Accepted Answer

$$P(	ext{wait} \u003e 7) = (10 - 7) 	imes 0.10 = 0.30$$

Question 3

Given a normal distribution with mean $$\mu = 50$$ and standard deviation $$\sigma = 5$$, what is the z-score for $$x = 62$$?

Accepted Answer

$$z = \frac{62 - 50}{5} = 2.4$$

Question 4

If $$P(Z  1.27)$$?

Accepted Answer

$$P(Z \u003e 1.27) = 1 - 0.8980 = 0.1020$$

Question 5

A researcher finds that the 90th percentile of a normal distribution corresponds to $$z \approx 1.28. If $$the mean exam score is 80 and the standard deviation is 6, what is the exam score at the 90th percentile?

Accepted Answer

$$x = 80 + (1.28)(6) = 87.68$$

Question 6

Which of the following is true about the sampling distribution of the sample mean $$\bar{x}$$?

Accepted Answer

It is centered at the population mean $$\mu.$$

Question 7

The standard error of the mean is given by which formula?

Accepted Answer

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

Question 8

If the population distribution is strongly right-skewed, which of the following is true about the sampling distribution of the sample mean for $$n = 50$$?

Accepted Answer

It will be approximately normal due to the Central Limit Theorem.

Question 9

A sample of 36 students has a mean study time of 12 hours per week. If the population mean is 10 hours and the population standard deviation is 6 hours, what is the z-score for this sample mean?

Accepted Answer

$$z = \frac{12 - 10}{1} = 2.00$$

Question 10

Which of the following best describes an unbiased estimator?

Accepted Answer

An estimator whose mean equals the population parameter it estimates.

Question 11

Which of the following is NOT a property of the standard normal distribution?

Accepted Answer

It is always right-skewed.

Question 12

A population has $$\mu = 100$$ and $$\sigma = 20. $$What is the probability that a randomly selected individual has a value less than 110? (Use the standard normal table: $$z = 0.5$$, $$P(Z \u003c 0.5) = 0.6915)$$

Accepted Answer

0.6915

Question 13

Which of the following is the correct formula to convert a z-score back to a raw value $$x$$?

Accepted Answer

$$x = \mu + z\sigma$$

Question 14

Which of the following is true about the sampling distribution of the sample variance $$s^2$$?

Accepted Answer

It tends to be right-skewed.

Question 15

A histogram of a data set is roughly symmetric, unimodal, and bell-shaped, and the normal Q-Q plot shows points close to a straight line. What is the best conclusion?

Accepted Answer

It is reasonable to assume the population is approximately normal.

Question 16

If a sample statistic systematically overestimates the population parameter, what can be said about the estimator?

Accepted Answer

It is biased upward.

Question 17

Which of the following is the correct z-score formula for a sample mean $$\bar{x}$$ from a sample of size $$n$$?

Accepted Answer

$$z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$$

Question 18

A biologist measures the mass of seeds from a greenhouse and finds they are approximately normal with $$\mu = 250 mg $$and $$\sigma = 30 mg. $$What mass separates the heaviest 10% of seeds?

Accepted Answer

$$x = 250 + (1.28)(30) = 288.4 mg$$

Question 19

Which of the following is NOT a step in finding the probability for a raw value from a normal distribution?

Accepted Answer

Multiply the z-score by the mean.

Chapter 6 Study Guide

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