how do you find the normal distribution between two values

Question

What percentage of the fittings have diameters between 7.0 cm and 8.0 cm if the mean diameter is 7.5 cm and the standard deviation is 0.5 cm?

Answer 1

Hello, thank you for taking the time to post your question!

You can actually just estimate this one based on the Empirical Rule … we are going 1 standard deviation from the mean in either direction and according to the Empirical Rule 68% of the data falls within one standard deviation of the mean

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Claudia,

z_L=(7-7.5)/.5=-1

z_U=(8-7.5)/.5=1

 

Using the table for the area of the normal curve  for z between -1 and +1 gives .6827 so the percentage of fittings in this range is 68.27

 

Jim