# Unique Distribution

If a balanced die is rolled six times and the outcomes create a unique distribution, perform the following:

P(exactly three fives) {Use formula}

mean {Use formula}

variance {use formula}

standard deviation {use formula}

Problem # 2

If 20% of the bolts produced by a machine are detective, then out of eight randomly chosen bolts find the following

P(three defective bolts) {use TI 83}

P(zero defective bolts) {use TI 83}

mean

variance

standard deviation

Problem #3

If a coin is tossed six times and the outcomes create a unique distribution perform the following:

Fill in the distribution table (x, P(x))

P(more than four heads)

P(at least three heads)

P(less than two heads)

Use the table in each case.

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If a balanced die is rolled six times and the outcomes create a unique distribution, perform the following:

P(exactly three fives) {Use formula}

mean {Use formula}

variance {use formula}

standard devaiation {use formula}

Solution.

(1) Denote the number of times the five occurs by X, then X follows binomial distribution with parameter n=6 and p=1/6, ie., X~b(6,1/6). So,

So, ...

#### Solution Summary

The solution discusses how a balanced die is rolled six times and the outcomes create a unique distribution.