Q: In a class of 30 students, two committee positions are to be filled without replacement. What is the probability that a randomly selected student is chosen for both positions?

$$\frac{1}{30} \times \frac{1}{29}$$

Q: Given a probability distribution with values x: 1, 2, 3 and probabilities P(x): 0.2, 0.5, 0.3, what is the mean?

$$1 \times 0.2 + 2 \times 0.5 + 3 \times 0.3 = 2.1$$

Q: A fair coin is flipped 10 times. What is the probability of getting exactly 7 heads?

$$\binom{10}{7} \times (0.5)^7$ \times (0.5)^3$

Q: A normal distribution has mean $$\mu=70$$ and standard deviation $$\sigma=10. $$What is the minimum score required to be in the top 10%?

$$x = \mu + z \sigma$$,\ z \approx 1.28$$,\ x = 70 + 1.28 \times 10 = 82.8$$

Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a value calculated from a population, while a statistic is a value calculated from a sample.

Question 2

A researcher records the blood types (A, B, AB, O) of 100 patients. What is the level of measurement for this data?

Accepted Answer

Nominal

Question 3

Which of the following is an example of quantitative data?

Accepted Answer

Temperature in degrees Celsius

Question 4

Given the following frequency distribution for the number of books read by students: 0 books: 5 students, 1 book: 10 students, 2 books: 15 students, 3 books: 20 students. What is the relative frequency for students who read 2 books?

Accepted Answer

$$\frac{15}{50}$$

Question 5

A histogram shows a distribution of exam scores that is skewed to the left. Which of the following statements is most accurate?

Accepted Answer

The mean is likely less than the median.

Question 6

Given the data set: 2, 4, 6, 8, 10. What is the midrange?

Accepted Answer

$$\frac{2+10}{2} = 6$$

Question 7

A sample of five test scores is: 70, 75, 80, 85, 90. What is the range?

Accepted Answer

$$90 - 70 = 20$$

Question 8

In a class of 30 students, two committee positions are to be filled without replacement. What is the probability that a randomly selected student is chosen for both positions?

Accepted Answer

$$\frac{1}{30} 	imes \frac{1}{29}$$

Question 9

A restaurant receives 60 orders. The probability that an order is accurate is 0.95. What is the probability that at least one order is inaccurate?

Accepted Answer

$$1 - (0.95$$)^{60}$$

Question 10

Given a probability distribution with values x: 1, 2, 3 and probabilities P(x): 0.2, 0.5, 0.3, what is the mean?

Accepted Answer

$$1 	imes 0.2 + 2 	imes 0.5 + 3 	imes 0.3 = 2.1$$

Question 11

A fair coin is flipped 10 times. What is the probability of getting exactly 7 heads?

Accepted Answer

$$\binom{10}{7} 	imes (0.5)^7$ 	imes (0.5)^3$

Question 12

In a binomial experiment with $$n=20$$ and $$p=0.1$$, which outcome is considered significantly low?

Accepted Answer

An outcome where the probability of obtaining that number of successes or fewer is less than 0.05.

Question 13

A continuous uniform distribution ranges from 2 to 8. What is the probability that a randomly selected value is between 4 and 6?

Accepted Answer

$$\frac{6-4}{8-2} = \frac{2}{6} = \frac{1}{3}$$

Question 14

For a standard normal distribution, what is the probability that $$z is $$between $$-1$$ and $$1$$?

Accepted Answer

Approximately $$0.68$$

Question 15

A normal distribution has mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What is the probability that a randomly selected value is less than 85?

Accepted Answer

$$P(x \u003c 85) = P(z \u003c \frac{85-100}{15}) = P(z \u003c -1)$$

Question 16

If 5 samples of size $$n=4$$ are taken from a population with mean $$\mu=50$$, and the sample means are 48, 52, 49, 51, and 50, what is the mean of the sample means?

Accepted Answer

$$\frac{48+52+49+51+50}{5} = 50$$

Question 17

A normal distribution has mean $$\mu=70$$ and standard deviation $$\sigma=10. $$What is the minimum score required to be in the top 10%?

Accepted Answer

$$x = \mu + z \sigma$$,\ z \approx 1.28$$,\ x = 70 + 1.28 	imes 10 = 82.8$$

Question 18

A company has 500 employees. The mean salary is $$\60$$,000$$ with a standard deviation of $$\$$10,000. $$What is the expected number of employees earning more than $$\75$$,000$?

Accepted Answer

Find $$z = \frac{75,000-60,000}{10,000} = 1.5$$. $$P(x \u003e 75,000) = 1 - P(z \u003c 1.5) \approx 0.0668. $$Expected number: $$500 	imes 0.0668 = 33.4$$

Question 19

A population has mean $$\mu=100$$ and standard deviation $$\sigma=20. $$What is the probability that a randomly selected value is between 90 and 110? What is the probability that the sample mean of $$n=25 is $$between 90 and 110?

Accepted Answer

For individual: $$z_1$$ = \frac{90-100}{20} = -0.5$$, z_2$ = \frac{110-100}{20} = 0.5$$. $$P(-0.5 \u003c z \u003c 0.5) \approx 0.3829. $$For sample mean: $$\sigma_{\bar{x}} = \frac{20}{\sqrt{25}} = 4$$. $$z_1$$ = \frac{90-100}{4} = -2.5$$, z_2$ = \frac{110-100}{4} = 2.5$$. $$P(-2.5 \u003c z \u003c 2.5) \approx 0.9876$$

Introductory Statistics Midterm Exam Study Guide

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