# Probability

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In a game at a fraternity party, there are 10 bottles to knock down. Five fraternity brothers line up to shoot the bottles down, each a perfect shot. Each brother selects one bottle at random and shoots. Find the e-value of your distribution of the number of bottles knocked down.

Each brother is a perfect shot so the probability of a brother knocking down their bottle = 1.

The brothers select a bottle at random so more than one brother can target the same bottle.

Mulitple Choice Answers:

a) 3.4

b) 4.1

c) 4.6

d) 5.0

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##### Solution Summary

In a game at a fraternity party, there are 10 bottles to knock down. Five fraternity brothers line up to shoot the bottles down, each a perfect shot. Each brother selects one bottle at random and shoots. Find the e-value of your distribution of the number of bottles knocked down.

Each brother is a perfect shot so the probability of a brother knocking down their bottle = 1.

The brothers select a bottle at random so more than one brother can target the same bottle.

Mulitple Choice Answers:

a) 3.4

b) 4.1

c) 4.6

d) 5.0

##### Solution Preview

Solution. We label 10 bottles. By the hypothesis "Each brother selects one bottle at random and shoots" we know that each bottle can be knocked down by these five brothers(one, two, three ,four of five of them) with the same probability p.

Define the i-th variable Xi as follows:

Xi=1 if the i-th bottle was knocked down; otherwise, ...

###### 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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