MA207 Assignment 5: The Normal Approximation

In Assignment 4 you computed the mean and standard deviation of a column from the EPA test card data.

Assume the data in your column can be reasonably approximated by a normal distribution with the mean and standard deviation that you computed in Assignment 4.

Use the NORMDIST spreadsheet function to answer the following questions (depending on the contents of your column):

If your column contained miles per gallon:

• Use the normal approximation to estimate the proportion of vehicles tested that get 20 miles per gallon or less.
• Use the normal approximation to estimate the proportion of vehicles tested that get 25 miles per gallon or more.
• Use the normal approximation to estimate the proportion of vehicles tested that get between 18 and 23 miles per gallon.
• Use the normal approximation to estimate the proportion of vehicles tested that get less than 20 or more than 30 miles per gallon.

If your column contained vehicle weight:

• Use the normal approximation to estimate the proportion of vehicles tested that weigh 4000 pounds or less.
• Use the normal approximation to estimate the proportion of vehicles tested that weigh 5000 pounds or more.
• Use the normal approximation to estimate the proportion of vehicles tested that weigh between 3500 and 4500 pounds.
• Use the normal approximation to estimate the proportion of vehicles tested that weigh less than 3200 or more than 5100 pounds.

If your column contained horsepower:

• Use the normal approximation to estimate the proportion of vehicles tested have 210 horsepower or less.
• Use the normal approximation to estimate the proportion of vehicles tested that have 300 horsepower or more.
• Use the normal approximation to estimate the proportion of vehicles tested that have between 250 and 400 horsepower.
• Use the normal approximation to estimate the proportion of vehicles tested that have less than 200 or more than 350 horsepower.

If your column contained cubic inches displacement:

• Use the normal approximation to estimate the proportion of vehicles tested that have 190 cubic inches or less.
• Use the normal approximation to estimate the proportion of vehicles tested that have 280 cubic inches or more.
• Use the normal approximation to estimate the proportion of vehicles tested that have between 220 and 350 cubic inches.
• Use the normal approximation to estimate the proportion of vehicles tested that have less than 150 or more than 380 cubic inches.

If your column contained number of cylinders:

• Use the normal approximation to estimate the proportion of vehicles tested have 6 cylinders or less.
• Use the normal approximation to estimate the proportion of vehicles tested that have 8 cylinders or more.
• Use the normal approximation to estimate the proportion of vehicles tested that have between 4 and 6 cylinders.
• Use the normal approximation to estimate the proportion of vehicles tested that have less than 4 or more than 6 cylinders.