# Thread: Probability and Averages

1. ## Probability and Averages

The prompt is this.

"The prices of power tools manufactured by Whammo are known to be normally distributed with a mean of $1200 and a standard deviation of$220. Suppose that I am the buying agent for my company and I need to buy 10 power tools from Whammo. If each tool is selected randomly what is the probability that I will be able to keep the average price for the power tools below \$1250? "

I have determined that probability of a single purchase by doing (1250-1200)/220 = .23 and from there I used a Z table to find the single probability is 0.591

My problem is I do not know how (and have not been able to find) the correct formula to find the average when it is applied 10 times. Appreciate any help anyone can provide.

2. ## Re: Probability and Averages

In short: If , then

In a more general framework:
- Every affine transformation of a multivariate normal random vector also follows a multivariate normal distribution
- A set of independent univariate normal is jointly following a multivariate normal distribution, and their covariance matrix is just a diagonal matrix
- Univariate normal is a special case of the multivariate normal distribution

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