How to make a normal distribution using the following parameters: mean, standard error, minimum, and maximum?

I need to create a 400x1 array that contains a normal distribution with a mean of 100, minimum of around 50 and maximum of around 150. I also have a standard error value of 0.05. I have tried creating a random number generator using normfit with mu = 100 and SD = 0.05. However, this just gives me a distribution with 400 elements all +/- 0.05 away from 100. I need a distribution that has the highest frequency around 100 and the lowest/highest around 50 and 150, respectivley. The SE isnt as important to me.

[Torsten]

I need a distribution that has the highest frequency around 100 and the lowest/highest around 50 and 150,

Unclear. If the highest frequency is around 100, then both at 50 and 150 are equal (usually low) frequencies.

[Sean]

Yes, the values at the 95% intervals, around 50 and 150, should have equally low occuring frequecies

[Torsten]

Then play with the variance to get the histogram you like.

If the random numbers must all lie in [50 150], use a truncated normal:

https://de.mathworks.com/help/stats/prob.normaldistribution.truncate.html

Answer 1

[dpb]

" have a standard error value of 0.05."

I have always heard "standard error" as being the std/mean -- using 0.05 as the standard deviation would imply

Z=(150-100)/0.05

Z = 1000

for which

1-normcdf(Z)

ans = 0

is so small as to be returned as identically zero.

OTOH, if it is a standard error of 5%, then the std dev would be 0.05*100 --> 5 and

Z=(150-100)/5

Z = 10

for which

1-normcdf(Z)

ans = 0

which is also still far too small for a normal to have any significant probability of values out that far.

The 95% Z values for a normal is

z=norminv([0.95 0.975])

z = 1×2

1.6449 1.9600

for one-sided or two-sided respectively, for which then the std deviation of your sampled distribution would need to be

s=(150-100)./z

s = 1×2

30.3978 25.5107

histfit(randn(400,1)*s(2)+100)