Normal Distribution and Percentiles

Which colored curve has the lowest standard deviation?

• Orange

• Red

• Blue

• Green

The weights of miniature horses are roughly normally distributed with a mean of 230 pounds and standard deviation of 45 pounds.
What proportion of miniature horses weigh between 95 and 365 pounds? 

• 50%

• 68%

• 95%

• 99.7%

The weights of miniature horses are roughly normally distributed with a mean of 230 pounds and standard deviation of 45 pounds.
What proportion of miniature horses weigh between 185 and 320 pounds? 

• 68%

• 25%

• 95%

• 81.5%

Below is a list of weights of 10 puppies, determine the percentile of a 5 pound puppy. 
2, 3, 3, 4, 4, 5, 5, 5, 6, 7

• 80th Percentile

• 70th Percentile

• 50th Percentile 

• 7th Percentile

Tests in Mr. Jones class have a mean score of 73 and standard deviation of 6 points. Mark scored a 68 on the test. What is his z-score?

• 0.83

• 5

• -0.83

• -5

Mile times for 2nd hour PE have an average of 9.5 minutes with a standard deviation of 0.8 minutes. Jessica's PE teacher told her that her time was 1.5 standard deviations below the mean. What was her time in minutes?

• 10.3 minutes

• 10.7 minutes

• 8.3 minutes

• 8.7 minutes

If the mean of a data set is 18 and the standard deviation is 3. What original data value has a z-score of -1.2?

• 21.6

• 16.8

• 14.4

• 21

A data set has a mean of 22. If x=16 has a z-score of -2, what is the value of σ?

• -3

• 3

• 1

• You cannot tell σ, if the data isn't normally distributed. 

If x=12 has a z-score of 2.2 and the standard deviation is 3, what is the value of μ?

• 18.6

• 5.4

• 15

• 9

What does a z-score of 2.15 mean?

• The score is 2.15 units above the mean. 

• The score is 2.15 standard deviations above the mean.

• The score is 2.15 units below the mean. 

• The score is 2.15 standard deviations below the mean.