Question

Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. use the given values of n and p to find the mean muμ and standard deviation sigmaσ. ​also, use the range rule of thumb to find the minimum usual value mu minus 2 sigmaμ−2σ and the maximum usual value mu plus 2 sigmaμ+2σ.

Answer 1

A binomial distribution is an experiment where there are two outcomes; Success and failure. For instance, you are given n = 128 and p = 0.27. The formula for the variance of a binomial distribution is n*p(1 – p) or n*p*q*. They are equivalent because q = 1- p. We will use the first equation.

 

Variance = n*p*(1 – p)

Variance = 128*0.27*(1 – 0.27)

Variance = 25.23

 

To get the standard deviation, find the square root of the variance.

Standard deviation = sqrt (Variance)

Standard deviation = sqrt (25.23)

Standard deviation = 5.02