Empirical Rule and Z-Score

What is the area under the curve between z = 0 and z = 1.45?

• .9265

• .4265

• .4500

• .5000

What is the total area under the curve?

• 1
• .9998
• .997
• -3 < z < 3

What is the probability that a score is above (right of) 2.37?

• .0116

• .0089

• .0068

• .0051

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 2.3 and 3.5?

• 68%

• 99.7%

• 95%

• 84%

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What is the GPA of the highest 2.5% of the students?

• 4.1 

• 4.1 or higher

• 4.7

• 4.5 or higher

Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. How common is a score between 600 and 700? Calculate the probability. 

• 2.5%

• 2.35%

• 16%

• 13.5%

In a population, if μ=125 and σ=25, how common are values in the 100 – 175 range?

• 68%

• 84%

• 81.5%

• 95%

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.

•  28,000 km and 32,000 km.

• 24,000 km and 34,000 km.

• 26,000 km and 34,000 km.

• 27,000 km and 31,000 km.

The average waist size for teenage males is 29 inches with a standard deviation of 2 inches. 
If waist sizes are normally distributed, determine the z-score of a teenage male with a 33 inch waist.  

• 2

• 1

• -2

• -1

Which best describes the shaded part of this normal distribution graph?

• All data that is one or higher.

• All data that is one or more standard deviations above the mean.

• All data that is between 1 and 3.

• All data that is above the mean.