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.

Please see attachment for the full solution.

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, …

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