Question

Use the Normal model N(1163,66) for the weight of streers.

a) what weight represents the 36th percentile?

b) what weight represents the 97th percentile?

c) what’s the IQR of the weights of these steers?

Answer 1

a) Given P(X < x) =0.36

We first convert N(1163,66) to standard normal N(0,1)

So P( X < x) =   

P(Z < z) = 0.36 , where z =

From Standard Normal tables we find z corresponding the probability 0.36, z = -0.36

pounds.

b) Proceeding as in part a. z corresponding the probability 0.97, z = 1.88

Solving pounds

c) IQR (Inter-quartile range ) = 3rd quartile - 1st quartile

To get the first quartile - , We solve for P(Z<z) = 0.25

z corresponding the probability 0.25, z = -0.675

To get the third quartile-, z corresponding the probability 0.75, z= 0.675

So IQR = 0.675 - (-0.675) = 1.35 or,

1207.55 - 1118.45 = 89.1