Q : A computer while calculating correlation coefficient between 25 pairs of two variables and x and y, obtained the following constants :
N=25 x = 125 x2 = 650 y = 100 y2 = 460 xy = 508
A recheck showed that the computer has occupied wrongly two pairs (6,14) and (8,6) of values of (x,y) instead of the correct values (8,12) and (6,8) respectively. Obtain the correct value of the correlation coefficient.

Ans :

Q : The Probability that a certain kind of component will survive a given shock test is 2/5. Find the probability that exactly three of the next five components tested will survive, using Binomial Distribution.

Ans :

5. Probability Calculation

In a bolt factory Machines A, B and C manufacture respectively 25, 35 and 40 percent of the total. Out of their total output 5, 4 and 2 percent are defective. A bolt drawn from the procedure at random is found to be defective. What is the probability that it is manufactured by (i) factory A (ii) factory C ?

Ans  :

         

The probability that the  BOLT is manufactured by

 (i) factory A   =  0.36 or 36 %

 (ii) factory C  =  0.23 or 23 %

( For Detail Calculation see the next table, where Baye’s Theorem Principle has been used )

The Following table shows  the monthly.

Draw the Pie Chart of the monthly expenses

Pie Chart is the graphical representation of data where shares of different items are shown as Sectors in proportion to their percentage in total share of all the items.  Let us calculate the Angles for Different items.  Total expense is represented by 360 degree.

3. FORTRAN Program for Mean, Minimum and Maximum Calculation

Write a FORTRAN subroutine MMM that computes the mean, the minimum and the maximum of an array A of N real numbers and prints out the values with suitable messages.

Ans :

It is assumed that the Main or Calling Programs will read the N, the size of the array and values of  array A and no read statements are required for N and A(N) in the subroutine MMM .

Here is listing of the Program:-

C*****SUBROUTINE MMM (A,N)

     C***** COMPUTE THE MEAN & PRINT ITS VALUE

           SUM = 0

      DO 10 I=1,N

 10  SUM = SUM + A(I)

      SMEAN = SUM/N

           WRITE(*,*) ‘THE MEAN VALUE = ‘,SMEAN

C***** COMPUTE THE MINIMUM & PRINT ITS VALUE

           SMIN = A(1)

      DO 20 I=2,N

      IF SMIN .LT. A(I) THEN SMIN = A(I)

 20   CONTINUE 

           WRITE(*,*) ‘THE MINIMUM VALUE = ‘,SMIN

C***** COMPUTE THE MAXIMUM & PRINT ITS VALUE

           SMAX = A(1)

      DO 20 I=2,N

      IF SMAX .GT. A(I) THEN SMAX = A(I)

 20   CONTINUE 

           WRITE(*,*) ‘THE MAXIMUM VALUE = ‘,SMAX

      RETURN

           END

. FORTRAN Program for Factorial Calculation

Write a FORTRAN Function FACT with one Integer parameter N, that computes the factorial of N and prints suitable message.

Ans :

FUNCTION FACT(N)

C*****INITIALISE FACT FOR N 

IF (N .LE. 0) THEN

FACT = 0

WRITE (*,*) ‘N <=0 AND FACT = 0′

GO TO 100

ELSE FACT = 1

END IF

DO 50 I=1,N

50          FACT = FACT*I

C***** PRINT RESULTS

WRITE (*,*)’THE FACTORIAL OF NUMBER N=’,N,’IS=’,FACT   

100          RETURN  

END