P(a < X < b), equations like this generally written as P(X < b) - P(X < a).
hope this helps
So, my problem is:
Let X be birth weight of a randomly chosen child in Norway, given in gram, g. Assume that
X is normally distributed, where E(X) = 3315 and Var(X) = 5752
a) Calculate the following probabilities,
1) P(X > 3000) 2) P(3000 < X < 3500) 3) P(X > 3500 | X > 3000)
What I have done to solve it:
So, I managed to get the right answer on 1, and I thought I would get the right answer on number 2.
I thought: P(3000 < X < 3500) = P(X > 3000) ∩ P(X < 3500). In 1) I calculated that P(X > 3000) is 0,709, this was correct. I calculated that P(X < 3500) = 0,6235. So 0,709 x 0,6235 = 0,4421 , but the right answer is: 0,335. What am I doing wrong?
Thanks for taking a look!
Ok, . This is the sum principle. If and , then it is guaranteed that . So, . Now, . If , then your data is wrong. If , then .
Oh, I see. For your answer in part 1, you have . What is ? It is the compliment of . So, . Now, as you wanted.