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**1. Homework Statement**

You have 7 apples whose weight (in gram) is independent of each other and normally distributed, N([itex]\mu[/itex]= 150, [itex]\sigma[/itex]

^{2}= 20

^{2}).

You also have a cabbage whose weight is independent of the apples and N(1000, 50

^{2})

What is the probability that the seven apples will weigh more than the cabbage?

**2. Homework Equations**

Let X represent the weight of the seven apples combined, and Y the weight of the cabbage.

X~N(1050, 2800)

Y ~N(1000, 50

^{2})

**3. The Attempt at a Solution**

I have an easy time calculating the probability that a random variable will yield a number within a specific interval. For example I know how to get the probability that the 7 apples will weigh more that 1000g,

p(X > 1000) =

[itex]\varphi[/itex](X > (1000 - [itex]\mu[/itex]

_{X})/[itex]\sigma[/itex]

_{x}) =

[itex]\Phi[/itex](0.94) = 0.8264, which I got from a chart for [itex]\Phi[/itex](x).

I am completely lost however on how to calculate the probability that a certain random variable will yield a bigger number that another random variable, both normally distributed but with different parameters: p(X > Y).

Thank you.

**1. Homework Statement**

**2. Homework Equations**

**3. The Attempt at a Solution**