Problem- Solving Exercise #1 Part A Roll a single standard six-sided die 36 time

Question

Problem- Solving Exercise #1

Part A

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 s tand deviation of your data.

Part B

Roll a pair of standard six-sided dice 36 times and tabulate your reuslt (i.e,s number of 2's number of 3's,...., number of 12's) Calculate the mean, variance standard deviation of your data.

Part C

Suppose you have a pair of six-sided dice where each die contains the following sides: (1,1,2,2, 3,3) In theory, if you rolled this pair of dice 36 times, how many times would you obtain a total of 2,3,4,5, and 6? Using graph paper, plot the distribution of expected values. Calcu;ate the mean, variance, and standard deviation of this distribution.

Part D

The number of false fire alarm in a suburb of Detroit averages 4.3 per day. Assumeing that a Poisson distribution is appropriate:

What is the probablility that exactly 4 false alarms will occur on a given day?

What us the probablity that less than 4 false alarms will occur a given day?

What is the probablity that more than 4 false alarms will occur on a given day?

(Hint: the probabilites of all possible cases must add to one)

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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