# Thread: P( |b1 - b2 |> 0.1) = 2p( b1 - b2 > 0.1)

1. ## P( |b1 - b2 |> 0.1) = 2p( b1 - b2 > 0.1)

Can any one tell me
How we can write P( |B1 - B2 |> 0.1)
equals to 2P( B1 - B2 > 0.1)

2. Originally Posted by Sashikala
Can any one tell me
How we can write P( |B1 - B2 |> 0.1)
equals to 2P( B1 - B2 > 0.1)
This is clearly not a chat topic. It's a statistics question and would better belong in one of the two statistics subforums.

What is B1? A random variable? What distribution does it follow? What is B2? The whole question is needed, not just the small scraps you've decided are important.

3. ## Statistics

B1,B2 are random variables and they follow normal distribution.
The full question is:
Bottles of mineral water are delivered to shops in crates containing 12 bottles each. The weights of bottles are normally distributed with mean weight 2kg and standard deviation 0.05kg. The weights of empty crates are normally distributed with mean 2.5kg and standard deviation 0.3kg.
Two bottes are selected at random from a crate. Find the probability that they differ in weight by more than 0.1kg.

4. Originally Posted by Sashikala
B1,B2 are random variables and they follow normal distribution.
The full question is:
Bottles of mineral water are delivered to shops in crates containing 12 bottles each. The weights of bottles are normally distributed with mean weight 2kg and standard deviation 0.05kg. The weights of empty crates are normally distributed with mean 2.5kg and standard deviation 0.3kg.
Two bottes are selected at random from a crate. Find the probability that they differ in weight by more than 0.1kg.
Let B1 and B2 be the random variables weight of first bottle and second bottle. You know they are both normally distributed with mean and standard deviation as given.

Then B = B1 - B2 is also a normally distributed random variable. Its mean is zero and standard deviation is $0.05 \sqrt{2}$. Read section 3 of this: Normal distribution - Wikipedia, the free encyclopedia

Calculate Pr(-0.1 < B < 0.1) = 2 Pr(0 < B < 0.1) by symmetry.

5. ## Statistics

Mr Fantastic
Thanks very much.

6. We always have P( |B1 - B2 |> 0.1)=P( B1 - B2> 0.1)+P( B1 - B2 <- 0.1).
NOW, if this random variable B1 - B2 is symmetric then those two probabilities are equal and you do get
=2P( B1 - B2> 0.1).

7. ## Statistics

MathEagle,
Thanks very much.