Question

X is normal variate with mean 30 and s.D. 5, find the probabilities that

Answer 1

Answer:

What is meant here by area is the area under the standard normal curve.

a) For x = 40, the z-value z = (40 - 30) / 4 = 2.5

Hence P(x < 40) = P(z < 2.5) = [area to the left of 2.5] = 0.9938

b) For x = 21, z = (21 - 30) / 4 = -2.25

Hence P(x > 21) = P(z > -2.25) = [total area] - [area to the left of -2.25]

= 1 - 0.0122 = 0.9878

c) For x = 30 , z = (30 - 30) / 4 = 0 and for x = 35, z = (35 - 30) / 4 = 1.25

Hence P(30 < x < 35) = P(0 < z < 1.25) = [area to the left of z = 1.25] - [area to the left of 0]

= 0.8944 - 0.5 = 0.3944