Use the normal model n(1133,78) for the weights of steers. a) what weight represents the 42nd percentile? b) what weight represents the 91st percentile? c) what's the iqr of the weights of these steers?

Step-by-step explanation:

Let .

Here, the mean is 1133 and standard deviation is 78.

Since we don't have the table for N(1133, 78), so we use the standard table for N(0,1),

a)

All we have to do is find, within the table the specific percentile.

now to find (42nd percentile) 0.42 in the normal table N(0,1) and extract the number on the row and column.

Using: where is the mean and is the standard deviation.

let

then, we have

Now, using Standard Normal table to find the value of z- score;

Usually, tables are set up as the probability that a number, z  is less than or equal to Z.

i.e,

Now, putting this value in  , to find x;  

On Simplify,  we get;

pounds

b)

Similarly, find the weight for 91st percentile.

Follow the same steps that we have done in part (a),

or

⇒

let

then, we have

Now, use normal table value to find the z-score;

Usually, tables are set up as the probability that a number, z is less than or equal to Z

we have, z= 1.34

putting the z value in   we get,

On simplify, we get

x= 1,237.52 pounds

c)

the interquartile range (IQR)=3rd Quartile - 1st quartile

First find the 1st quartile:

⇒

let

then, we have

Now, we use normal table to find that z=-0.675

putting the z value in   we get,

On simplify, we get

x= 1,080.35 pounds

Similarly, for third quartile

By symmetry z=0.675

putting the z value in   we get,

On simplify, we get

x= 1,185.65 pounds

then, IQR = 1185.65 -1080.35=105.3 pounds