Normal Probability

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%

In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval?

• 1084 to 1216 pounds 

• 1106 to 1150 pounds 

• 1106 to 1194 pounds 

• 1128 to 1172 pounds

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.

If the value we are looking for is smaller than the mean, the value of z is:

• Not enough information

• Negative

• Positive

• 0

If the value we are looking for is the same as the mean, the value of z is:

• Not enough information

• Positive

• Negative

• 0

The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds.  What is the z-score for a player who runs a time of 5.6 seconds?

• -1.33

• 1.33

• 0.0918

• 0.9082

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5.  What proportion of weeks would you expect to have less than 5 accidents?

• 0.6915

• 0.1762

• 0.8238

• -0.93

According to the empirical rule, what percentage of data falls within 1 standard deviation? 

• 25%

• 68%

• 95%

• 99.7%

According to the empirical rule, how much of the data falls within 3 standard deviations? 

• 25%

• 68%

• 95%

• 99.7%

What shape is a normal distribution curve?

• Half curve

• Round curve

• Bell curve

• Square curve