0.8157
To find this probability we must calculate the value of a cumulative distribution function for the normal random variable X, with parameters µ and σ. We can reduce this calculation to one concerning the standard normal random variable Z as follows:
FX(x) = P(X ≤ x) = P(Z ≤ "\\frac{x-\u03bc}\u03c3" ) = FZ("\\frac{(x-\u03bc)}\u03c3" )
This last expression can be found in a table of values of the cumulative distribution function for a standard normal random variable.
In our case μ = 3252, σ = 614, x = 3804, so we have
P(X < 3804) = P(X ≤ 3804) = FZ("\\frac{3804-3252}{614}" ) = FZ(0.8990) = 0.8157.
Comments
Leave a comment