Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    1
    ReputationRep:
    The random variable X has a normal distribution with mean 21 and standard deviation 5 (b) Find the value of w such that P(X > w | X > 28) = 0.625


    So far I have done the following:

    X ~ N (21 , 5^2)

    P(X > w | X > 28) = P(X > w ∩ X > 28) / P (X > 28)

    Z = (X - 21)/5
    Z = 1.4

    P(Z>1.4) = 1 - P(Z<1.4)
    = 0.0808


    P(X > w ∩ X > 28) / 0.080 = 0.625
    P(X > w ∩ X > 28) = 0.0505


    Where do I go from this point?
    Offline

    10
    ReputationRep:
    Nice work with the first part of the problem!

    The way I would think about the last part is this:
    Since P(X > w | X > 28) = 0.625, w must be greater than 28. (If w<28 then P(X > w | X > 28) would be 1).

    Since w > 28, the event {X>w AND X>28} is included in the event {X>w>28}.

    Hence P(X > w ∩ X > 28) = P(X > w).
    So now you simply need to solve P(X > w) = 0.0505 using the standard normal distribution like you did before
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by square_peg)
    Nice work with the first part of the problem!

    The way I would think about the last part is this:
    Since P(X > w | X > 28) = 0.625, w must be greater than 28. (If w<28 then P(X > w | X > 28) would be 1).

    Since w > 28, the event {X>w AND X>28} is included in the event {X>w>28}.

    Hence P(X > w ∩ X > 28) = P(X > w).
    So now you simply need to solve P(X > w) = 0.0505 using the standard normal distribution like you did before
    Thank you for your help
 
 
 
Poll
Who is your favourite TV detective?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.