you can use your own data for part A and part B Roll a single standard six-sided

Question

you can use your own data for part A and part B

Roll a single standard six-sided die 36 times and tabulate your results (i.e., number of 1's number of 2's, ..., number of 6's). Calculate the mean, variance and standard deviation of your data. Roll a pair of standard six-sided dice 36 times and tabulate your results (i.e., number of 2's, number of 3's, ..., number of 12's). Calculate the mean, variance and standard deviation of your data. Suppose you have a pair of six-sided dice where each die contains the following sides: (1, 2, 2, 3, 4, 4). In theory, if you rolled this pair of dice 36 times, how many times would you obtain a total of 2, 3, 4, 5, 6, 7, and 8? Using graph paper, plot the distribution of expected values. Calculate the mean, variance, and standard deviation of this distribution. The number of false fire alarms in a suburb of Detroit averages 3.1 per day. Assuming that a Poisson distribution is appropriate: What is the probability that exactly 3 false alarms will occur on a given day? What is the probability that less than 3 false alarms will occur on a given day? What is the probability that more than 3 false alarms will occur on a given day?

Explanation / Answer

Part A:

PArt C

X f P(X) X*P(X) X^2*P(X) 1 5 0.1389 0.1389 0.1389 2 6 0.1667 0.3333 0.6667 3 4 0.1111 0.3333 1.0000 Mean = X P(X) 3.667 4 8 0.2222 0.8889 3.5556 Variance X^2 P(X)- ^2 2.778 5 7 0.1944 0.9722 4.8611 SD SQRT(Var) 1.667 6 6 0.1667 1.0000 6.0000 36 1.0000 3.6667 16.2222

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