STATZIKI

Input

More or Equal to

P(Z > -2.5) = 0.99379

Less or Equal to

P(Z < -2.5) = 0.00621

When do you use the normal distribution?

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take large random samples from a population, then the distribution of the sample will be approximately normally distributed.

In addition, you can use the normal distribution as an approximation to the binomial distribution and the poisson distribution.
-If X ~ B(n, p) and if n is large then x is approximately normally distributed with variance = np(1-p), a good rule of thumb is if np(1-p) > 5 you may want to use the normal distribution.
-If x ~ Po(μ) then for large values of of μ you may want to use the normal distribution, a good rule of tumb is if μ > 5.

Example, The weekly amount of money spent on maintenance and repairs by a company was observed, over a long period of time, to be approximately normally distributed with mean $400 and standard deviation σ $20. If $450 is budgeted for next week, what is the probability that the actual cost will exceed the budgeted amount?