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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