# Working with probability in the given situation given x-bar and sample size.

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Your troop's past cookie sales went sour last year. Parents had to bail you and your troop member out of the hole. For next year the troop wants to know from your customers the planned cookie orders are likely to be for the next year.

You get x-bar = $160,000

s = $80,000 and n = 1000.

What is the probability that the real average is at least $150,000?

What is the probability that the real average is between $150,000 and $175,000?

The troop will go bust/bankrupt if the average is less than $125,000. How worried should the troop be? Are there at least two variables or sources that bias the data? Finally, if the number is greater than $175,000 more scouts are likely to join. Does that mean that the troop is doing better and others will want to join?

Why or why not?

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Your troop's past cookie sales went sour last year. Parents had to bail you and your troop member out of the hole. For next year the troop wants to know from your customers the planned cookie orders are likely to be for the next year.

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Let X be a random variable denoting the number of the planned cookie orders and assume that X follows normal distribution

N(a,b^2) where a is the mean of X(i.e., E(X)=a) and b is the standard deviation.

According to the hypothesis, by the point estimation we can use the mean of sample xbar to estimate value a and use the ...

###### 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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