SOLUTION: A die is rolled 300 times. Find the mean and variance of the number of 1's that show. Please show work and explain. Thanks :)

Algebra ->  Probability-and-statistics -> SOLUTION: A die is rolled 300 times. Find the mean and variance of the number of 1's that show. Please show work and explain. Thanks :)      Log On


   

Question 601709: A die is rolled 300 times. Find the mean and variance of the number of 1's that show.
Please show work and explain. Thanks :)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
P(rolling a 1) = 1/6

Let that probability be p.

Mean:

mu = np

mu = 300*(1/6)

mu = 300/6

mu = 50


So the mean number of 1's that should show is 50 (ie you should expect to roll a one on a single die 50 times)

-----------------------------

Variance

sigma^2 = np(1-p)

sigma^2 = 300*(1/6)*(1 - 1/6)

sigma^2 = 300*(1/6)*(5/6)

sigma^2 = (300*1*5)/(1*6*6)

sigma^2 = 1500/36

sigma^2 = 125/3

sigma^2 = 41.667

So the variance is 41.667