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# Stats 3 normal distributions, 2 variables Watch

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1. Hi,

I have a question about normal distributions, which seems really easy initially, but it involves 2 variables.

There are 2 ways to pay electricity

Method 1: fixed charge of £10 and a charge of 6.45p per unit used
Method 2: no fixed charge, charge of 7.88p per unit used

Number of units used by Anne has a normal distribution with mean 920 and standard deviation 95.
Number of units used by Baz has a normal distribution with mean 750 and standard deviation 64.

Given that Baz uses method 2 and Anne uses method 1, find the probability that Baz pays more than Anne. Assume that the amounts of electricity used by Anne and Baz are independent.

Let number of units used by Anne be x and number used by Baz be y.

Then we need to find P(7.88y - 1000 - 6.45x > 0 )

I have no idea how to progress seeing as we have two different random variables. The answer is 0.0985 is that helps.

2. Linear Combination of Random Variables?
3. (Original post by Rational Paradox)
Linear Combination of Random Variables?
Ahhh, thank you!!

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Updated: December 28, 2010
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