The distance is 10 meters. What is the variable?

The distance between two points needs to be measured, in meters. The true distance
between the points is 10 meters, but due to measurement error we can’t measure the
distance exactly. Instead, we will observe a value of 10+ϵ
ϵ, where the error ϵ
ϵ is distributed
(0,0.04)
N(0,0.04). Find the probability that the observed distance is within 0.4 meters of the
true distance (10 meters). Give both an exact answer in terms of Φ
Φ and an approximate
numerical answer.

Because the dept in the ocean