Suppose the expected tensile strength of type-A steel is 103 ksi and the standard deviation of tensile strength is 7 ksi. For type-B steel, suppose the expected tensile strength and standard deviation of tensile strength are 105 ksi and 5 ksi, respectively. Let X^- = the sample average tensile strength of a random sample of 80 type-A specimens, and let Y^- = the sample average tensile strength of a random sample of 60 type-B specimens.
a. What is the approximate distribution of X^-? Of Y^-?
b. What is the approximate distribution of (X^-) - (Y^-)? Justify your answer.
c. Calculate (approximately) P(-1<_ X^- - Y^- <_1)

a

i So  the approximate distribution of is and  

ii So the approximate distribution of is and  

b

 the approximate distribution of   is and  

Here we can see that the mean of the approximate distribution is negative which tell us that this negative value of the  data for   sample   are more and their frequency occurrence is higher than the positive values  

c

the value of   is    

Step-by-step explanation:

From the question we are given that

       The expected tensile strength of the type A steel is  

        The standard deviation of type A steel is  

         The expected tensile strength of the type B steel is

            The standard deviation of type B steel is  

Also the assumptions are

       Let be the sample average tensile strength of a random sample of 80 type-A specimens

Here

      Let be  the sample average tensile strength of a random sample of 60 type-B specimens.

  Here

Let the sampling distribution of the mean be

 Let the sampling distribution of the standard deviation be

So What this mean is that the approximate distribution of is and  

For

 The sampling distribution of the sample mean is

  The sampling distribution of the standard deviation is

So What this mean is that the approximate distribution of is and                        

Now to obtain the approximate distribution for

The standard deviation of is

Now to find the value of  

  Let us assume that

Using the z-table to obtain their z-score

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3

linear pair postulates