Q: A college admits only students with SAT Reading scores in the top 10%. If SAT scores are normally distributed with $$\mu = 500$$ and $$\sigma = 100$$, what is the minimum score required?

$$x = 500 + 1.28 \times 100 = 628$$

Q: A college-bound senior wants to be in the top quarter of ACT scores. If the mean ACT score is 20.8 and the standard deviation is 4.8, what is the minimum score required?

$$x = 20.8 + 1.40 \times 4.8 = 27.52$$

Question 1

An SAT section has a mean score of 500 and a standard deviation of 100. If a student scores 650, what is their z-score?

Accepted Answer

$$z = \frac{650 - 500}{100} = 1.5$$

Question 2

Which of the following statements about shifting all data values by a constant is TRUE?

Accepted Answer

Measures of spread (standard deviation, range, IQR) are unchanged.

Question 3

A cereal manufacturer wants no more than 4% of boxes to be underweight (less than 16.0 oz). If the mean is set at 16.2 oz, what standard deviation is required?

Accepted Answer

$$\sigma = \frac{16.2 - 16.0}{1.75} \approx 0.114$$

Question 4

If you multiply all data values by 2, what happens to the mean and standard deviation?

Accepted Answer

Both the mean and standard deviation are multiplied by 2.

Question 5

A college admits only students with SAT Reading scores in the top 10%. If SAT scores are normally distributed with $$\mu = 500$$ and $$\sigma = 100$$, what is the minimum score required?

Accepted Answer

$$x = 500 + 1.28 	imes 100 = 628$$

Question 6

Which of the following is NOT a condition for using the Normal model?

Accepted Answer

The data must be categorical.

Question 7

If a value has a z-score of $$-2.5 in a $$standard normal distribution, what can you say about its position?

Accepted Answer

It is far below the mean, in the lower tail of the distribution.

Question 8

A student scores 680 on the SAT Math section ($$\mu = 500$$, $$\sigma = 100). $$What percent of students scored below this value?

Accepted Answer

About 97.7%

Question 9

What is the formula for calculating a z-score?

Accepted Answer

$$z = \frac{y - \bar{y}}{s}$$

Question 10

Using the 68-95-99.7 rule, what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 11

A manufacturer sets the mean weight of cereal boxes at 16.35 oz with a standard deviation of 0.2 oz. What percent of boxes will be underweight (less than 16.0 oz)?

Accepted Answer

About 4%

Question 12

If the mean SAT score is 500 and the standard deviation is 100, what is the probability that a randomly selected score is between 450 and 600?

Accepted Answer

About 53.28%

Question 13

Which of the following best describes the effect of converting data to z-scores?

Accepted Answer

The mean becomes 0 and the standard deviation becomes 1.

Question 14

A college-bound senior wants to be in the top quarter of ACT scores. If the mean ACT score is 20.8 and the standard deviation is 4.8, what is the minimum score required?

Accepted Answer

$$x = 20.8 + 1.40 	imes 4.8 = 27.52$$

Question 15

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

Accepted Answer

$$\mu ($$population mean)

Question 16

If a distribution is not unimodal and symmetric, what is the best course of action before applying the Normal model?

Accepted Answer

Check the Nearly Normal Condition using a histogram or Normal probability plot.

Question 17

Which of the following is TRUE about the standard Normal distribution?

Accepted Answer

It has a mean of 0 and a standard deviation of 1.

Question 18

A value is 1.66 standard deviations above the mean. What is its z-score?

Accepted Answer

$$z = 1.66$$

Question 19

If the mean and standard deviation of a dataset are 168.93 seconds and 2.90 seconds, respectively, what are the mean and standard deviation in minutes?

Accepted Answer

Mean: $$2.8155$$ min, SD: $$0.0483$$ min

Standard Deviation as a Ruler and the Normal Model

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