Mathematical P and x

Question

P(x>77.6)=

P(x<70.9)=

P(73.7<x<78.6)=

n=74

mean=75

standard deviation x =2

Answer 1

use transformation to standard normal distribution:

z = (x - mean)/standard deviation):

P(x > 77.6) = P(z > (77.6 - 75)/2) = P(z > 1.3) = P(z < -1.3) = 0.0968.

P(x < 70.9) = P(z < (70.9 - 75)/2) = P(z < -2.55) = 0.0054.

P(73.7 < x < 78.6) = P((73.7 - 75)/2 < z < (78.6 - 75)/2) = P(-0.65 < z < 1.8) = P(z < 1.8) - P(z < -0.65) = 0.9641 - 0.2578 = 0.7064.