Answer:
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