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# Unique Distribution

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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 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))

Use the table in each case.

##### Solution Summary

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

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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, ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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