- #1
Gauss M.D.
- 153
- 1
Homework Statement
The number of hours of sunshine in one week in a specific resort is assumed to follow a normal distribution with expectation 43 and standard deviation 17.
Family A will spend the first three weeks of the summer at the resort. Family B will spend the LAST two weeks of the summer at the resort.
Assuming everything is independent, what is the probability that family A will get atleast twice as much sunshine as family B?
Homework Equations
A = # of sunshine hours for family A
B = # of sunshine hours for family B
The Attempt at a Solution
E(A) = 3*E(X) = 129
σ(A) = sqrt(3)*σ(X) = 29.4
E(B) = 86
σ(B) = sqrt(2)*σ(X) = 24
So A ~ N(129, 29.4), B ~ N(86, 24)
If we let Z = A/B and try to find P(Z > 2), we do not have a linear combination of normally distributed random variables so I guess that's not the right way to go, assuming we want to do the normal table reading thing. So I don't know where to go from here. Help!