Characteristics
Applying the Percentage Rule
Empirical rule
z–Scores
Probabilities
100
The shape of the graph of a normal distribution is this.
What is bell-shaped?
100
A normal distribution has a mean of 8 and a standard deviation of 2. The value that is 2 positive standard deviations away from the mean is this.
What is 12?
100

The percentage of data that falls within one standard deviation of the mean.

What is 68%

100

The formula for determining z-scores is this.

What is "data value - mean ÷ standard deviation"?

100

The percentage of data that falls in the range greater than z = 1.15. 

What is 0.5 - 0.3749 = 0.1251 x 100 = 12.51%

200
This measure of central tendency of a normal distribution represents the highest point on the curve
What is the mean?
200
A normal distribution has a mean of 15 and a standard deviation of 3. The value that is 3 negative standard deviations away from the mean is this.
What is 6?
200

The percent of data that is within 2 standard deviations of the mean.

What is 95%

200

The sign of the z-score of any data point that falls BELOW the mean.

What is negative.

200

The area under the normal curve to the left of z=1.58.

What is 0.5 + 0.4430 = 0.9430?

300
These percentages roughly represent the percent of the data values that fall within one, two, and three standard deviations from the mean of a normal distribution.
What is 68–95–99.7%?
300
A normal distribution has a mean of 10 and a standard deviation of 1. The percentage of data values that fall between the values of 8 and 12 is this.
What is 95%?
300

The percentage of data that falls within 3 standard deviations of the mean.

What is 99.7%?

300

A normal distribution has a mean of 7 and a standard deviation of 2.5. What is the z–score that corresponds to a data value of 10 for this distribution.

What is 1.2?

300

The probability of a z-score to the left of z = –1.38 is this.

What is 0.5 – 0.4162 = 0.0838?

400
The curve is this with respect to its mean.
What is symmetric?
400
A normal distribution has a mean of 24 and a standard deviation of 6. 68% of the values of this distribution fall between what two data values?
What is 18 and 30?
400

The percent of data that lies outside one standard deviation of the mean.

What is 32%?

400
A normal distribution has a mean of 84 and a standard deviation of 4. The percentage of the data of this distribution that falls below 78 is this.
What is 6.68%?
400

Calculate the percentage of data between z=0.47 and z=2.46.

What is 0.4931 - 0.1808 = 0.3123 x 100 = 31.23%

500
The total area under the curve of a normal distribution is this.
What is one?
500
A normal distribution has a mean of 100 and a standard deviation of 10. The percentage of data values that fall between the values of 70 and 90 is this.
What is 15.85?
500

The percentage of data that lies between the mean and one standard deviation above the mean.

What is 34%

500

The data value (x) corresponding to a normal distribution with a mean of 25, standard deviation of 1.2 and a z-score of 55.7.

What is 91.84?

500

Calculate the percentage of data between z=-0.63 and z=1.44.

What is 0.2357 + 0.4251 = 0.6608 x 100 = 66.08%

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