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

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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#### Solution Preview

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 ...

#### Solution Summary

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.