Assume the random variable \(\mathrm{x}\) is normally distributed with mean \(\mu=86\) and standard deviation \(\sigma=4\). Find the indicated probability.
$$ \begin{array}{r} P(75<x<80) \\ P(75<x<80)= \end{array} $$
(Round to four decimal places as needed.)
Solution:- P( 75 < x < 80) = 0.0638
Mean = 86, S.D = 4
x1 = 75
x2 = 80
By applying normal distribution:-
z1 = - 2.75
z2 = -1.50
P( -2.75 < z < -1.50) = P(z > -2.75) - P(z > -1.50)
P( -2.75 < z < -1.50) = 0.997 - 0.9332
P( -2.75 < z < -1.50) = 0.0638
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