Suppose that the weight of a person selected at random from

Suppose that the weight of a person selected at random from some population is normally distributed with parameters µ and . Suppose also that P(X 160) =1/2 and P(X 140) =1/4. Find:

i. µ and

ii. P(X 200)

Solution

P(X 160) =1/2 and P(X 140) =1/4.

i.e. z value for 160 = 1/2 or mu = 160 (Since normal distribution is symmetrical about mean.)

When mean =160

z value for 140 = (140-160)/sigma = z value for 1/4

i.e. -20/sigma = -0.675

sigma =20/0.675 =29.630

-------------------------------------------------------

ii) P(X>=200) = P(Z>=1.35) = 0.5-0.4115

= 0.0885