quantitative math question

Question

Assume that you have a normal distribution representing the likelihood of completion times. The mean of the distribution is 10, and the standard deviation is 3. True or False: The probability of completing the project in 8 or fewer days is the same as the probability of completing the project in 18 days or more.

Answer 1

Hi Nicole,

 

A normal distribution is symmetric, so the probability of values more extreme than two different values will occur if they are both the same distance from the mean in opposite directions.

 

For example, if your distribution had a mean of 0, then getting a number higher than 5 or lower than -5 would have the same probability.

 

This question gives a situation with a mean of 10. Are 8 and 18 the same distance away from 10?

 

You don't need the standard deviation to compare these probabilities, but you do need it if you're going to calculate the probabilities. You need a z-chart or statistics-capable calculator to find those values.