Normal Distribution and Percentiles

What does σ represent?

• sample standard deviation
• population/distribution standard deviation
• sample mean
• population/distribution mean

What does μ represent?

• sample standard deviation
• population/distribution standard deviation
• sample mean
• population/distribution mean

What value(s) must you include when defining a normal distribution?

• μ
• σ
• both μ and σ
• 68, 95 and 99.7

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

Anna and her brother are both 62 inches tall. Anna is in the 85th percentile for height for her age and her little brother is in the 90th percentile. Who is taller for their age?

• They're the same, both 62 inches.
• Anna, she's taller than more people. 
• Brother, he's taller than more people. 
• You can't tell if you don't know the mean and standard deviation. 

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