3. Male and female hourly wages have distributions Wm ~ N(13, 4) and W; ~ N(14,9),...

Question

Question

3. Male and female hourly wages have distributions Wm ~ N(13, 4) and W; ~ N(14,9), respectively. (a) Wm and Wf denote male an

business economics

Answer 1

Answer #1

Solution:

ANSWER:

a)

Let Z = 2Wm + 3Wf

Mean Z = 2(13) + 3(10)

= 26 + 30 = 56

Var (Z) = 2² Var(Wm) + 3² Var(Wf)

= 4(4) + 9(9) = 97

Thus, Z ~ N(56, 97)

If the covarience was 6,

then:

Mean (Z) = 56 (as before)

Var (Z) = 2² Var(Wm) + 3² Var(Wf) + 2 Cov (2Wm, 3Wf)

= 4(4) + 9(9) + 2(2) (3) (6)

= 169

Z ~ N(56, 169)

b)

P ( Wf > 11)

= P ( Z > 11 - 10 / sqrt(9) ) where Z = standard normal variate

= P ( Z > 1/3)

= 0.3694

Answer 2

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