# Exam 2, 311

What is the z score for scores in the bottom 5%?

-1.645

A researcher records the following data for the number of bids made on a sample of items sold at an auction. Based on the table, what was the probability that an item had 7 bids made on it? Number of Bids Frequencies 3/5 4/12 5/7 6/6 7/10

.25

The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making more than five errors.

.29

The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making at most two errors.

.43

A therapist goes through her records and finds that 200 of her 400 patients showed significant improvement in mental health over the past year. Hence, the probability of her patients showing significant improvement in mental health is

.50

The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making at least three errors.

.57

In a game, the probability of winning money is p = .16, the probability of losing money is p = .54, and the probability of breaking even is p = .30. What is the probability of winning or losing money in this game?

.70

(Note: The beginning of this problem is the same "story" for the next 3 problems, too) The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making at most five errors.

.71

A researcher selects a sample of size 4 from a population of size 6. How many possible samples of this size can be selected using experimental sampling?

15

A researcher reports that the probability of a college student living on campus is p = .38. If a small local college has 2,000 students enrolled, then what is the standard deviation of college students living on campus? Hint: This is a binomial probability distribution.

21.7 students

EXTRA CREDIT!!! How many possible samples of size 2 can be selected from a population of 5 using theoretical sampling?

25

A researcher wants to know the probability of being named on the honor roll from a population where 8% of students are on the honor roll. If the researcher selects a sample of 400 students, then what is the mean number of students expected to be on the honor roll? Hint: This is a binomial distribution, where p = 0.08 and q = 0.92.

32

A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20. About 68% of the sample means in this sampling distribution should be between a sample mean of

36 and 40

A researcher determines that the probability of missing class among students at a local school is p = .16. Assuming that the school has 300 students enrolled, how many students can we expect to miss class on a given day? Hint: This is a binomial probability distribution.

48 students

A normal distribution has a mean equal to 53. What is the standard deviation of this normal distribution if 2.5% of the proportion under the curve lies to the right of x = 66.72? (Round your answer to two decimal places)

7.00

If the standard deviation of a probability distribution is 9, then the variance is

81

What does it mean to say that the sample mean is an unbiased estimator of the population mean?

If we select a sample at random, then on average we can expect the sample mean to equal the population mean.

Which of the following is NOT a characteristic of probability?

Probability is most useful for describing fixed events.

A researcher selects two samples of 64 participants each. In the first sample the population mean was 10 and the variance was 16. In this second sample, the population mean was 25 and the variance was 9. Which sample will be associated with a larger standard error of the mean?

Sample 1

State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the left of z = 0.80, or the area to the right of z = -0.80.

The two areas are the same

What values are distributed along the x-axis for a sampling distribution of the sample mean?

sample means

(2 pts). How are probability and relative frequency related?

They are the same thing.

Suppose that a researcher selects a sample of participants from a population. If the shape of the distribution in this population is positively skewed, then what is the shape of the sampling distribution of sample means?

approximately normally distributed

The ________________theorem explains that the shape of a sampling distribution of sample means tends toward a normal distribution, regardless of the distribution in the population

central limit

Bayes' theorem is often applied to a variety of ________ probability situations, including those related to statistical inference.

conditional

When the probability of one outcome changes depending on the occurrence of a second outcome, these outcomes are referred to as

conditional

The mean of the sampling distribution of sample means is

equal to the population mean

A researcher selects a sample of 16 participants from a population with a variance of 4. What is the standard error of the mean?

less than 1

Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities?

multiplicative rule

The following distribution most closely approximates a

normal distribution

The probability of a college student being employed is p = .35. The probability of a student being employed and dropping out of college is p = .20. Hence, the probability of a student dropping out of college, given that he or she is employed, is

p = .57

Regardless of the shape of the distribution in the population, the sampling distribution of sample variances approximates a

positively skewed distribution

The proportion or fraction of times an outcome is likely to occur is referred to as

probability

What values are distributed along the x-axis for a sampling distribution of the sample variance?

sample variances

A _________________ distribution of the sample means is a distribution of all possible sample means that can be obtained in samples of a given size (n) from a population (N).

sampling

For the experimental sampling strategy,

sampling is without replacement

The normal distribution is symmetrical, which means that

scores above the mean are distributed the same as scores below the mean

Scores far from the mean are located in the ________ of a normal distribution.

tails

What is the implication for the tails of a normal distribution being asymptotic?

that extreme scores are possible in a normal distribution

Each of the following statements are true, except that

the larger the sample size, the larger the standard error

EXTRA CREDIT!!! Increasing the number of observations or samples in a study will decrease the standard error (standard error of the mean). This is known as

the law of large numbers

Two outcomes are said to be mutually exclusive when

the probability of the two outcomes occurring together is equal to zero (p = 0)

Each of the following is an example of a binomial distribution, except

the time it takes to complete a driving test

The normal distribution has all of the following characteristics, except

the total area under the curve is greater than 1.0

How is the standard error of the mean typically reported in a graph?

using error bars

The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a

z score

(4 pts) Given two outcomes, A and B, state their relationship as a conditional probability using a "given" statement. (Hint: Be sure to state BOTH possible conditional probabilities).

(2pts): the probability of A, given that B occurs, (2pts) the probability of B, given that A occurs

(4 pts) Assume number of days absent is normally distributed. If a sample mean is 8 and SD is 2, what's the z-score for a person with 2 days absent?

-3

The standard normal distribution is normally distributed with a mean of ____ and a variance of ____.

0; 1

Which proportion is largest in a z distribution?

The proportion of area between z = +1 and z = -1.