To standardize data for a z test, you first subtract the _____ from each term in a data set.
a)Mean b)median c) Mode
M - Marge is in the room
C - Bart eats chips
D - Bart eats donuts.
Each probability is conditional on Bart eating either chips or donuts.
P(M) = P(M\C)P(C) + P(M\D)P(D).
rearranging the equation to solve for P(D), you get:
P(D) = [P(M)-P(M\C)P(C)]/P(M\D)
We don't know what P(C) is, but we do know that it is the complement of P(D), so instead of P(C) write 1-P(D)
P(D) = [.46 - .40(1-P(D))]/.60
First step: (Distribute -.40)
P(D) = [.46 - .40 + .40P(D)] / .60
Next step, combine like terms (.46-.40)
P(D) = [.06 + .40P(D)] / .60
Now write .06 and .40P(D) each as its own separate fraction over .60
P(D) = .06/.60 + .40P(D)/ .60
Step #4 - Simplify the fractions
P(D) = 1/10 + 2/3P(D)
Step #5 - sub 2/3P(D) from both sides)
1/3 P(D) = 1/10
Final step - mult both sides by 3)
P(D) = 3/10.
That's Bart. Doing the equation a similar way for homer will get you:
P(D) = [.54 - .40(1-P(D))]/.60
P(D) = [.54 - .40 + .40P(D)] / .60
P(D) = [.14 + .40P(D)] / .60
P(D) = .14/.60 + .40P(D)/ .60
P(D) = 7/30 + 2/3P(D)
1/3 P(D) = 7/30
P(D) = 21/30, or in simplest form, 7/10.
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