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

Answer:

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 %