Probability Distributions: Master the Basics for Psychology

Question 1

The probability density function of the normal distribution is characterized as

Accepted Answer

bell-shaped and symmetric

Answer

skewed to the left

Answer

skewed to the right

Answer

uniformly distributed

Question 2

Which of the following is NOT an appropriate application of the t-distribution?

Accepted Answer

calculating the probability of a sample mean

Answer

testing hypotheses about the mean of a population

Answer

calculating confidence intervals for the mean

Answer

testing hypotheses about the difference between means of two populations

Question 3

Which scenario best exemplifies a binomial distribution?

Accepted Answer

Counting the number of heads obtained in 10 coin flips.

Answer

Measuring the heights of students in a classroom.

Answer

Recording the time taken to complete a maze.

Answer

Assessing scores on an intelligence test.

Question 4

In a t-test with a sample size of 15, what are the degrees of freedom?

Accepted Answer

14

Answer

15

Answer

30

Answer

60

Question 5

What is a distinctive characteristic of a normal distribution?

Accepted Answer

Symmetrical bell-shaped curve

Answer

Mean

Answer

Variance

Answer

Standard deviation

Question 6

What is the probability of obtaining a z-score less than -2.0 according to the standard normal distribution?

Accepted Answer

0.0228

Answer

0.9772

Answer

0.05

Answer

0.95

Question 7

What is the probability of rolling a 6 on a fair six-sided die?

Accepted Answer

1/6

Answer

1/3

Answer

1/4

Answer

1/5

Question 8

What is the mean of a binomial distribution with n = 10 trials and p = 0.5?

Accepted Answer

5

Answer

2.5

Answer

7.5

Answer

10

Question 9

Which of the following is NOT a defining characteristic of a normal distribution?

Accepted Answer

Bimodal

Answer

Symmetrical shape

Answer

Bell-shaped curve

Answer

Single peak (Uni-modal)

Question 10

Determine the mean of a binomial distribution with (n = 10) and (p = 0.4).

Accepted Answer

3

Answer

2.5

Answer

4

Answer

5

Question 11

Identify a key distinction between the binomial and normal distributions.

Accepted Answer

Discrete vs. Continuous nature

Answer

Mean of 1 vs. 0

Answer

Discrete data vs. Continuous data

Answer

Symmetrical vs. Skewed nature

Question 12

If two events, A and B, are independent, what is the probability of both events occurring?

Accepted Answer

Product of their individual probabilities

Answer

Sum of their individual probabilities

Answer

Quotient of their individual probabilities

Answer

Difference of their individual probabilities

Question 13

In a hypothesis testing situation, what is the probability of rejecting the null hypothesis when it is actually true? This is also known as:

Accepted Answer

Type I error

Answer

Type II error

Answer

Statistical significance

Answer

Power of the test

Question 14

Which of the following probability distributions is appropriate for modeling the number of successes in a sequence of repeated, independent trials?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Chi-square distribution

Question 15

In psychological research, which probability distribution is most commonly employed?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

t-distribution

Answer

Chi-square distribution

Question 16

What is the average value, or mean, of a standard normal distribution?

Accepted Answer

0

Answer

1

Answer

2

Answer

3

Question 17

In a binomial distribution, the expected number of successes is represented by:

Accepted Answer

np

Answer

np(1-p)

Answer

p(1-p)

Answer

1-p

Question 18

Which statement about the assumptions of the normal distribution is incorrect?

Accepted Answer

Mean and standard deviation must be known.

Answer

Data is continuous.

Answer

Distribution is symmetrical.

Answer

Distribution is bell-shaped.

Question 19

What is the fundamental distinction between a population distribution and a sampling distribution?

Accepted Answer

Population distribution is known, sampling distribution is estimated.

Answer

Sampling distribution is known, population distribution is estimated.

Answer

Population distribution is continuous, sampling distribution is discrete.

Answer

Sampling distribution is continuous, population distribution is discrete.

Question 20

Which of the following is the standard deviation (σ) for the binomial distribution?

Accepted Answer

σ = √(n * p * (1-p))

Answer

σ = n * p * (1-p)

Answer

σ = p / √(n * (1-p))

Answer

σ = n / √(p * (1-p))

Question 21

Which of the following is NOT a characteristic of the t-distribution?

Accepted Answer

Asymmetrical with a longer right tail for small degrees of freedom

Answer

Symmetrical about the mean

Answer

Unimodal

Answer

Bell-shaped

Question 22

Which of the following is true about the probability of a binomial distribution?

Accepted Answer

It is a discrete distribution that takes on values between 0 and n, where n is the number of trials.

Answer

It is a continuous distribution that can take on any value between 0 and 1.

Answer

It is a discrete distribution that can take on any positive integer value.

Answer

It is a continuous distribution that can take on any value between -1 and 1.

Question 23

Which of the following distributions is most appropriate for modeling the number of successes in a sequence of independent Bernoulli trials, where each trial has a fixed probability of success?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Exponential distribution

Question 24

What is the expected value of a binomial distribution with n trials and probability of success p?

Accepted Answer

E(X) = n * p

Answer

E(X) = 1 - n * p

Answer

E(X) = n

Answer

E(X) = p

Question 25

What is the shape of a t-distribution with a large number of degrees of freedom?

Accepted Answer

Symmetrical and bell-shaped, similar to the normal distribution

Answer

Skewed to the right

Answer

Skewed to the left

Answer

Bimodal

Question 26

A researcher aims to estimate the proportion of students who experience test anxiety in a university. Which type of probability distribution would be appropriate for modeling this scenario?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

t-distribution

Answer

Chi-square distribution

Question 27

The standard deviation of a distribution provides information about:

Accepted Answer

Spread or variability of the data

Answer

Mean or average value

Answer

Probability of obtaining a specific value

Answer

Kurtosis or peakedness of the distribution

Question 28

In a normal distribution, the probability of obtaining a value within one standard deviation of the mean is approximately:

Accepted Answer

68.3%

Answer

34.1%

Answer

50%

Answer

95%

Question 29

Which of the following values represents the probability of obtaining a z-score between -1.96 and 1.96?

Accepted Answer

0.95

Answer

0.05

Answer

0.09

Answer

0.99

Question 30

The t-distribution is typically used when:

Accepted Answer

The sample size is small and the population standard deviation is unknown

Answer

The population is normally distributed

Answer

The sample size is large and the population standard deviation is known

Answer

The proportion of successes is less than 0.5

Question 31

The formula for calculating the mean of a binomial distribution is:

Accepted Answer

n * p

Answer

n * q

Answer

p / q

Answer

q / p

Question 32

Which characteristic does NOT apply to the normal distribution?

Accepted Answer

Defined by one parameter

Answer

Symmetry around the mean

Answer

Bell-shaped curve

Answer

Kurtosis of 0

Question 33

In a standard normal distribution, what is the likelihood of obtaining a value between z = -1 and z = 1?

Accepted Answer

0.68

Answer

0.34

Answer

0.95

Answer

0.99

Question 34

Which test statistic is used for hypothesis testing with a t-distribution?

Accepted Answer

T-score

Answer

Z-score

Answer

F-score

Answer

Chi-squared score

Question 35

A researcher wants to examine the hypothesis that the mean IQ score of children exceeds 100. Which statistical test is appropriate?

Accepted Answer

One-sample t-test

Answer

Two-sample t-test

Answer

Chi-squared test

Answer

ANOVA

Question 36

A researcher is studying the number of times a student checks their phone during a lecture. The researcher believes that the number of checks follows a binomial distribution with a probability of success of 0.2. What is the probability that a student checks their phone exactly 5 times during a lecture?

Accepted Answer

0.066

Answer

0.1

Answer

0.4

Answer

0.2

Question 37

A researcher is conducting a hypothesis test to determine if the mean weight of a population of mice is different from 10 grams. The researcher collects a sample of 50 mice and finds that the sample mean is 11 grams with a sample standard deviation of 2 grams. What is the value of the t-statistic?

Accepted Answer

2.5

Answer

1

Answer

10

Answer

5

Question 38

A researcher is studying the distribution of IQ scores in a population. The researcher finds that the distribution is approximately normal with a mean of 100 and a standard deviation of 15. What percentage of scores would be expected to fall between 85 and 115?

Accepted Answer

68%

Answer

50%

Answer

34%

Answer

95%

Question 39

A researcher is studying the distribution of rainfall in a particular region. The researcher finds that the amount of rainfall follows a Poisson distribution with a mean of 5 inches per year. What is the probability that there will be more than 10 inches of rainfall in a given year?

Accepted Answer

0.0607

Answer

0.1

Answer

0.2

Answer

0.4