# I'm stuck with this hard probability question

• Dec 11th 2009, 11:20 AM
essedra
Normal Random Variables - Can anyone guide me to do the rest of the problem
A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with a mean of 89 meters and a standard deviation 190 meters.
What is the probability that the measured distance will be smaller than the true distance?

I interpreted the question as this: what is the probability that the "overestimate" is less than zero? (Do you think I interpreted it right?)

Then, I expressed the difference between the mean (89) and 0 as a number of standard deviations:
89/190= 0,4684

but now I'm stuck... Can anyone help me to do the rest of the question?

Appreciate any responds.
• Dec 11th 2009, 12:35 PM
mr fantastic
Quote:

Originally Posted by essedra
A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with a mean of 89 meters and a standard deviation 190 meters.
What is the probability that the measured distance will be smaller than the true distance?

I interpreted the question as this: what is the probability that the "overestimate" is less than zero? (Do you think I interpreted it right?)

Then, I expressed the difference between the mean (89) and 0 as a number of standard deviations:
89/190= 0,4684

but now I'm stuck... Can anyone help me to do the rest of the question?

Appreciate any responds.

Calculate Pr(X < 0) where X ~ Normal(mean = 89, sd = 190).