# A die is rolled 10 times and the number of twos that come up is tallied. If this experiment is repeated find the standard deviation for number of two?

##### 1 Answer

The standard deviation is

#### Explanation:

This experiment involves repeating identical independent trials (the rolling of the die), with the same condition for "success" each time (rolling a "2"). So, it will have a **binomial distribution**—this means the probability of rolling

#((n), (k))p^k(1-p)^(n-k)," "k=0,1,2,...,n#

Where:

#n# is the number of trials in the experiment (#10# ), and#p# is the probability of success in each trial (#1/6# ).

Binomial distributions have a *mean* of *standard deviation* of

#sigma = sqrt(np(1-p))=sqrt(10*1/6*(1-1/6))#

#color(white)(sigma = sqrt(np(1-p)))=sqrt(10*1/6*5/6)#

#color(white)(sigma = sqrt(np(1-p)))=sqrt(50/36)#

#color(white)(sigma = sqrt(np(1-p)))=sqrt((5^2*2)/6^2)#

#color(white)(sigma = sqrt(np(1-p)))=(5sqrt(2))/6# .