Question

QUESTION 9 Y is a random variable that is distributed N(5,12.96). Find k such that Prob(Y< 2.012 OR Y> k) 0.9356 QUESTION 10 Y is a random variable that is distributed N(-2,17.64). Find k such that Prob(Y <-10.19 OR Y> k)-0.0444 QUESTION 11 Y is a random variable that is distributed N(2,104.04). FIind Prob(-27.784 < Y<7.916).

Answer 1

C LURE VIEW THE FULNUY VUUWSTICI RR Console > round (pnorm(-0.83),4) [1] 0.2033 > round (qnorm (0.1389) *3.6+5,4) [1] 1.093 > 1-0.9356 [1] 0.0644 > (1-0.9356)/2 [1] 0.0322 > round (qnorm (0.0322) *3.6+5, 4) [1] -1.6578 > 0.2033+1-0.9356 [1] 0.2677 > round (norm (0.2677) *3.6+5,4). [1] 2.7688

granica P (Y< 2.012 or yk) = 0.9356 - P( 2 0 2 + P(xy) P(< << 2.012) = 0 9 3 5 6 Case-I [K72.012 then P (k <7 <2012) = 0. = (y22.012) + Plyk) = 0.9356

→ P (V< 2.012.) + P (Y>K) = 0,935 Ply-1295 12.96 , 20012-5). PY- & K-5 7 = 0.9356 12.96 ) $12.96 √ 12.96 ) P(Z <- 0.83) + P(Z > k. s ] = 0.9356. where Z~ N(0, 1) = (-0.83) + 1-(K) = 0.9356 → 0.2033 + 1 ) = 0.9356 » (3:6) - = *-0 K5 1939 1993] > K= 2.4688 (0.2677) 0.2677 K.5 s 11 K-5 3.6 01 3.6

Caso 2 (K < 2.012] then, P (Y22.012) + P (YK) - P(KLY 22.012) = 0.9356 P (Y 22.012) + P (YK) - P(Y.C2.012) - P(YLK) = 0.9356 - P(YLK) - P(YLK) = 0.93 56

X 1-2 (6) = 0.9356 → (2) - 1-02 -5 3.6 - 09356 1-5.0356 2. 型表 - k = 5+3.6 李 (p.6322) = -1-6518