X &#x223C;<!-- ∼ --> N ( 15 , 4 ) Find P( X > 18.7 | X > 11.7 ). Attemp

hard12bb30crg

hard12bb30crg

Answered question

2022-05-15

X N ( 15 , 4 )
Find P( X > 18.7 | X > 11.7 ).
Attempt: Rewrite as P ( x > 18.7) - P( x > 11.7)
Using the phi function
ϕ ( 1.85 ) ϕ ( 1.65 ) = ( 0.9678 ) ( 0.0495 ) = 0.9183
Where did I go wrong?

Answer & Explanation

aliasjuliankso9y

aliasjuliankso9y

Beginner2022-05-16Added 11 answers

Note that there is a difference between P ( A B ), being the chance that A and B happen both, and P ( A B ), being the chance of A happening, given that B happened. So you made a mistake in your definition of conditional probability.

Therefore, applying the correct definition, you will find that
p = P ( X > 18.7 X > 11.7 ) = P ( X > 18.7 X > 11.7 ) P ( X > 11.7 )
Hence we find that
p = P ( X > 18.7 ) P ( X > 11.7 ) .
We have that P ( X > 18.7 ) = P ( Z > 18.7 15 2 ) = P ( Z > 1.85 ) and P ( X > 11.7 ) = P ( Z > 1.65 ). Note that
P ( Z > 1.85 ) = 1 P ( Z 1.85 ) = 1 ϕ ( 1.85 ) = 1 0.9678 = 0.0322
and
P ( Z > 1.65 ) = P ( Z 1.65 ) = ϕ ( 1.65 ) = 0.951
where we could take the first equality because of symmetry of the normal distribution with respect to the y-axis.
Hence we find that
p = 0.0322 0.951 = 0.03386.
hard12bb30crg

hard12bb30crg

Beginner2022-05-17Added 3 answers

You should apply the Bayes theorem:
P ( X > 18.7 | X > 11.7 ) = P ( X > 18.7 X > 11.7 ) P ( X > 11.7 ) = P ( X > 18.7 ) P ( X > 11.7 ) = 1 P ( X 18.7 ) 1 P ( X 11.7 )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?