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. 

The weights of miniature horses are roughly normally distributed with a mean of 230 pounds and standard deviation of 45 pounds (SOURCE: https://www.scottcreek.com/mini-horse-facts.html).
What model would you use to describe the distribution of miniature horse weights?

• Normal: μ = 45, σ = 230
• Model T
• Normal: μ = 230, σ = 45
• Cindy Crawford

Which of the following is NOT part of the Empirical Rule (for normal distributions)?

• 95% of data is within 2 standard deviations of the mean
• 100% of data is within 4 standard deviations of the mean
• 68% of data is within 1 standard deviation of the mean
• 99.7 % of data is within 3 standard deviations of the mean

The following information applies to the next 6 questions: The weights of miniature horses is roughly normally distributed with a mean of 230 pounds and standard deviation of 45 pounds.
What proportion of miniature horses weigh more than 230 pounds? 

• 45%
• 50%
• 230 horses
• 68%

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 275 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 95 and 365 pounds? 

• 50%
• 68%
• 95%
• 99.7%