Question 1002049: You ask your graduate student to roll a die 10,000 times and record the results. Give the expected mean and standard deviation of the outcome. Part B: The die roll experiment is repeated (though with a different graduate student – for some reason your previous student went to work with a different advisor). However in this case, the die is weighted so that a 6 shows up 20% of the time and all remaining numbers show up 16% of the time. Now what is the mean and sd of 10,000 rolls?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! in a proportion, the mean is equal to np and the standard deviation is equal to sqrt(npq)
p is the probability of success.
q is the probability of failure.
q = 1 minus p
in a fair dice, probability of getting a 6 is 1/6 and probability of not getting a 6 is 5/6.
you get p = 1/6 and q = 5/6.
with 10,000 rolls, mean is np = 10,000 * 1/6 = 10,000/6.
standard deviation is sqrt(n*p*q) = sqrt(10,000 * 1/6 * 5/6) = sqrt(50,000/36).
in decimal form rounded to 2 decimal places, you have mean = 1666.67 and standard deviaton = 37.27.
when p = .2, you get:
p = 1/5 and q = 4/5.
n is still 10,000.
mean = np = 10,000 * 1/5 = 10,000/5.
standard deviation = sqrt(npq) = sqrt(10,000 * 1/5 * 4/5) = sqrt(40,000/25)
in decimal form rounded to 2 decimal places, you have mean = 2000 and standard deviation = 40.
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