Question

Assume the random variable X is normally distributed with mean = 50 and standard deviation = 7. Compute the probability, P(X > 35). Be sure to draw a normal curve with the area corresponding to the probability shaded.

Answer 1

P [ X > 35 ] = 0,983 or P [ X > 35 ] = 98,3 %

Step-by-step explanation: See Annex valid region for 98,3 in red lines

P [ X > 35 ] = 1 - P [ X ≤ 35 ]

P[ X ≤ z ] = ( X - μ₀ ) / σ

P [ X ≤ 35 ] = ( 35 - 50 ) / 7

P [ X ≤ 35 ] = - 15 / 7

P [ X ≤ 35 ] = - 2,1428

We find for z(score) = - 2,14 in z-table the value of 0,01618

P [ X ≤ 35 ] = 0,01618 or P [ X ≤ 35 ] ≈ 1,62 %

And

P [ X > 35 ] = 1 - 0,01618

P [ X > 35 ] = 0,983 or P [ X > 35 ] = 98,3 %