In the following table, construct a relative frequency distribution for the numb

Question

In the following table, construct a relative frequency distribution for the number of successes in four trials. In the second column, enter the number of times 0,1,2,3, and 4 successes were observed. In the third column, enter the proportion (relative frequency) of times 0,1,2,3, and 4 successes were observed.

In the fourth column, enter the probabilities. To find these probabilities, you can use your graphing calculator or the formula.

Show work to fill the fourth column. (In this case, the probability of success is =0.25).

Number of sucesses, x Number of families with x sucesses Proportion of families with x sucesses Theoritical Probability 0 6 .2 1 17 .567 2 3 .1 3 4 .133 4 0 0

Explanation / Answer

Formula: P(X = k) = nck * pk * (1-p)(n-k)

a) P(X = 0) = 0.754 = 0.3164

b) P(X = 1) = 4c1 * 0.25 * 0.753 = 0.4219

c) P(X = 2) = 4c2 * 0.252 * 0.752 = 0.2109

d) P(X = 3) = 4c3 * 0.253 * 0.75 = 0.0469

e) P(X = 4) = 4c4 * 0.254 * 0.750 = 0.0039

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