(a) CSM Instructor Dr. Probably rolls a fair, ten-sided die 1,000 times, and eac
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Question
(a) CSM Instructor Dr. Probably rolls a fair, ten-sided die 1,000 times, and each time records the number (from 1 through 10) that comes up. About what will the mean F of the resulting data set probably be? (b) Dr. P. flips 11 fair coins and records the number of heads that come up; Dr. P. repeats this experiment 1,000 times. About what will the mean F of the resulting data set probably be? (e) How will the standard deviations of the data sets in the above two experiments compare Please explain.Explanation / Answer
s a)
we have a fair dice having ten sides.
Hence the probability of each side coming up is 1/10
The possible numbers that comes up are 1,2,3,4,5,6,7,8,9,10
Therefore the mean of the data set in which the dice rolled is 1000 =
= 1 * (1/10) + 2 * (1/10) + 3 * (1/10) + 4 * (1/10) + 5 * (1/10) + 6 * (1/10) + 7 * (1/10) + 8 * (1/10) + 9 * (1/10) + 10 * (1/10)
= 55 / 10 = 5.5
5 b)
As the coin is fair the probability of heads coming up 0.5
For 11 coin tosses the number of heads to come up =
= 1 * 0.5 + 1 * 0.5 + 1 * 0.5 + 1 * 0.5 + 1 * 0.5 + 1 * 0.5 + 1 * 0.5 + 1 * 0.5 + 1 * 0.5 + 1 * 0.5 + 1*0.5
= 5.5
Repeating this data set for 1000 times the mean of the number of heads to come up will be = 5.5
Total heads coming will be 5.5 * 1000 = 5500
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