## Instructions

**Objective**

Write a program to create a histogram of random numbers chosen with normal distribution using Fortran 95 assignment solution.

## Requirements and Specifications

**Screenshots of output**

**Source Code**

```
PROGRAM Program1
IMPLICIT NONE
REAL, PARAMETER :: PI=3.14159265358979323846
INTEGER, PARAMETER :: NGEN1 = 13000
REAL, PARAMETER :: AVG1 = 22.0
REAL, PARAMETER :: STDDEV1 = 2.5
INTEGER, PARAMETER :: NGEN2 = 7000
REAL, PARAMETER :: AVG2 = 15.5
REAL, PARAMETER :: STDDEV2 = 1.0
INTEGER :: i
REAL :: n1, n2, ngauss
INTEGER :: new_seed;
! Read seed
print*, "Seed?"
read*, new_seed
! set seed for random generator
call srand(new_seed)
open(11,FILE="Bumps.txt", STATUS='REPLACE', ACCESS='SEQUENTIAL',ACTION='WRITE')
! Generate 13000 numbers with gaussian distribution
! with average= 22.0 and stddev = 2.5
do i = 1, NGEN1
! generate two numbers
n1 = rand()
n2 = rand()
! generate normally distributed number
ngauss = boxMuller(n1, n2, AVG1, STDDEV1)
write(11, *) ngauss
end do
! Generate 7000 numbers with gaussian distribution
! with average= 15.5 and stddev = 1.0
do i = 1, NGEN2
! generate two numbers
n1 = rand()
n2 = rand()
! generate normally distributed number
ngauss = boxMuller(n1, n2, AVG2, STDDEV2)
write(11, *) ngauss
end do
close(11)
CONTAINS
! generate a random number with gaussian distribution
! and given average m and standard deviation s, using
! the Box-Muller algorithm based on the uniformly
! distributed numbers n1 and n2
REAL FUNCTION boxMuller(n1, n2, m, s)
REAL, INTENT(IN) :: n1, n2, m, s
REAL :: r, z1
r = sqrt(-2.0 * log(n1))
z1 = r*cos(2.0 * PI * n2)
! transform to given median and deviation
boxMuller = m + s*z1
END FUNCTION boxMuller
END PROGRAM Program1
PROGRAM Program2
IMPLICIT NONE
INTEGER, PARAMETER :: NNUMBERS = 20000
REAL, PARAMETER :: HIST_MIN = 10
REAL, PARAMETER :: HIST_MAX = 30
INTEGER, PARAMETER :: HIST_NBOXES = 100
INTEGER :: i, box
REAL :: n, boxwid, start
INTEGER :: histogram(100)
! initialize histogram to zero
do i = 1, HIST_NBOXES
histogram(i) = 0
end do
! box size
boxwid = (HIST_MAX - HIST_MIN) / HIST_NBOXES
! Read the 20000 numbers from the file and
! build histogram with the data
open(11,FILE="Bumps.txt")
do i = 1, NNUMBERS
read(11, *) n
if (n >= HIST_MIN .and. n <= HIST_MAX) then
box = (n - HIST_MIN)/boxwid + 1
histogram(box) = histogram(box) + 1
end if
end do
close(11)
! write histogram to a file
open(12,FILE="BumpsHist.txt", STATUS='REPLACE', ACCESS='SEQUENTIAL',ACTION='WRITE')
do i = 1, HIST_NBOXES
start = (i - 1)*boxwid + HIST_MIN
write(12, *) start, histogram(i)
end do
close(12)
END PROGRAM Program2
Contact Details
```

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