Question 1

Suppose you add a constant $$c to $$every value in a dataset. Which of the following statements is TRUE about the effect on the dataset's standard deviation?

Accepted Answer

The standard deviation remains unchanged.

Question 2

A set of exam scores has a mean of 70 and a standard deviation of 8. If every score is multiplied by 1.5, what is the new standard deviation?

Accepted Answer

$$8 	imes 1.5 = 12$$

Question 3

Which of the following best describes the effect of multiplying every value in a dataset by a positive constant $$c$$?

Accepted Answer

Both the mean and standard deviation are multiplied by $$c.$$

Question 4

Given a dataset with mean $$\bar{y} = 50$$ and standard deviation $$s = 5$$, what is the $$z-$$score of an observation $$y = 65$$?

Accepted Answer

$$z = \frac{65 - 50}{5} = 3$$

Question 5

A student scores 1.5 standard deviations above the mean on a standardized test. What is the student's $$z-$$score?

Accepted Answer

$$z = 1.5$$

Question 6

Which of the following is NOT a characteristic of the Normal model?

Accepted Answer

It is always skewed to the right.

Question 7

If a variable $$Y$$ follows a Normal distribution $$N(100, 15)$$, what percentage of observations are expected to fall between $$85$$ and $$115$$?

Accepted Answer

About 68%

Question 8

A machine dispenses dye with a mean of $$\mu = 5.5 mL $$and standard deviation $$\sigma = 0.4 mL. If $$more than $$6 mL is $$unacceptable, what is the $$z-$$score for $$6 mL$$?

Accepted Answer

$$z = \frac{6 - 5.5}{0.4} = 1.25$$

Question 9

According to the 68-95-99.7 rule, approximately what percentage of data falls within two standard deviations of the mean in a Normal distribution?

Accepted Answer

About 95%

Question 10

IQ scores for adults aged 20 to 34 are approximately Normal with mean $$\mu = 110$$ and standard deviation $$\sigma = 25. $$What is the $$z-$$score for an IQ of $$160$$?

Accepted Answer

$$z = \frac{160 - 110}{25} = 2$$

Question 11

If a dataset is transformed by multiplying every value by $$2$$ and then adding $$5$$, what happens to the variance?

Accepted Answer

The variance is multiplied by $$4.$$

Question 12

Which of the following best describes a $$z-$$score of $$0$$?

Accepted Answer

The observation is equal to the mean.

Question 13

A dataset has a mean of $$20$$ and a standard deviation of $$4. If $$you add $$6 to $$every value, what are the new mean and standard deviation?

Accepted Answer

Mean: $$26$$, SD: $$4$$

Question 14

Which of the following is a parameter of a Normal model?

Accepted Answer

The mean $$\mu$$

Question 15

If a histogram of data is bell-shaped and symmetric, which model is most appropriate to describe the data?

Accepted Answer

Normal model

Question 16

A variable $$X is $$distributed as $$N(50, 10). $$What is the probability that a randomly selected value is greater than $$70$$?

Accepted Answer

About 2.5%

Question 17

If the standard deviation of a dataset is $$s$$, what is the standard deviation after all values are multiplied by $$-3$$?

Accepted Answer

$$3s$$

Question 18

Which of the following statements about the 68-95-99.7 rule is correct?

Accepted Answer

About 99.7% of data falls within three standard deviations of the mean.

Question 19

A researcher wants to compare test scores from two different exams with different means and standard deviations. What should she use to make a fair comparison?

Accepted Answer

Standardize the scores using $$z-$$scores.

Question 20

If a value is 2 standard deviations below the mean, what is its $$z-$$score?

Accepted Answer

$$z = -2$$

The Standard Deviation as a Ruler and the Normal Model

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