Calculating the Correlation Between Bert and Ernie's Wave Ride Times

[sam_0017]

The Correlation.. !??

Homework Statement

Bert and Ernie are trying to impress Lady Moneypenny with their surfing skills. Bert’s wave ride times are normally distributed with a mean of 15 seconds and a standard deviation of three seconds. Ernie spends more time drinking rather than practising his surfing, so his wave ride times are normally distributed with a mean 12 seconds and a standard deviation of 2 seconds. Due to natural changes in surfing conditions, Bert and Ernie’s wave ride times are positively correlated. Lady Moneypenny notices that Ernie’s wave ride time exceeds Bert’s 20% of the time. Determine the correlation between Bert and Ernie’s wave ride times.

---------

i tray to solve it be using this teaneck and i don't know is it correct :

since there are normally distributed :
B~(15,3²) R~(12,2² )

and we have P(B>R)= 20%

lat X= B-R , X~(μ ,λ)

μ=E [X] = E-E[R] = 15-12 = 3

and also:
λ= Var[X]= Var[B-R] = Var+Var[R]-2cov(B,R).
=9+4-2cov(B,R) =13-2cov(B,R). ... (*)

and from :
P(B,R)=$\frac{Cov(B,R)}{\sqrt{Var(B). Var(R)}}$

so:
Cov(B,R) = 6P(B,R)
by souping in (*):
λ=13-12P(B,R)

So now we have :
X~N(μ,λ) = X~N(3,13-12P(B,R))

and from the question P(B>R)= 20% so P(B-R>0)=20%
so we can say P(B-R>0)=P(X>0) = 0.2



... And here i stooped !?
can anyone help with this Question ??

 

[Nino MMP]

Homework EquationsP(B,R)=\frac{Cov(B,R)}{\sqrt{Var(B). Var(R)}}The Attempt at a Solution see the Question