Question

"A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with a mean of 8 meters and a standard deviation 64 meters. Suppose that the distance is measured by the radar four times and each of these four measurements is independent. A serious error takes place if average of these four independent measurements is not within 61 meters of the true distance (taking into account both underestimation and overestimation). What is the probability of a serious error?"

Answer 1

According to question,

A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with

Mean = 8 meters

and

Standard deviation = 64 meters

Now,

If the serious error take place when average of the four independent measurements is not within 61 meters of the true distance (taking into account both underestimation and overestimation) then the probability of a serious error is

= P(|x| > 61)

= P( x ≤ -61) + P( x ≥ 61)

= 0.1401 + 0.2033 = 0.3434

(Using standard normal distribution table)

Hence, the probability of serious error is 0.3434 or 34.34 % .