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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
Dec 31, 2016

Answer:

The standard deviation is #sqrt(10 * 1/6 * 5/6)= (5sqrt(2))/6#.

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 #k# 2's will be

#((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 #np#, and a standard deviation of #sqrt(np(1-p))#. Thus, the standard deviation #sigma# of this distribution is

#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#.