Question

2.5) Compute thc following probabilities: a. If Y is distributed N(1,4), find Pr(YS3). b. If Y is distributed N(3,9), find Pr(Y>0). *c. If Y is distributed N(50,25), find Pr(40 < Y S 52). d. If Y is distributed N(5,2), find Pr(6 SY S8).

Answer 1

(a) yN(,4) i.e P(ys3) P (Y PNCo) 3- y-s N(o,) 2 6 TEdagge 1-P (Ne)) o.15866 A. O-84134 (This value is from 1 nemal integral pbabili table OR directly Can we 0.84134 Fnm Excel formula NoRMSoIST (1

B I U at Painter Alignment Font f NORMSDIST(1) Formula Bar G C E H 0.841345

(ь) y- N( 3.s) g, 6-3 e -3, Usin centallimit ( r(Nn) thearem J Z Y NCo P(z-) A 1-P (z-) (Fram NaTmal prababili 1 o.JS865S o 841345 (1-9 P(z-) oR a IS8655 usinExel,

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25, 2as uso (c) y-N(so, 2s) e P (4752) S2-SO P-2 0.4) P/4-S - A C 1- P(z) - P(>4 1 P(z -2) - P (z<-o.4) o o.4 (P(e() ymme 1-o.o2275 o.34458 due to lo. 63267

FE Mer U at Painter Font Alignment -NORMSDIST(-2) Formula Bar G C B D E H 0.02275

Merge B IU Painter Alignment Font f NORMSDIST(-0.4) Formula Bar D B C 0.344578 LLJ

(d) YN(S,a) 2, .e. uS P(6y 8) 6- S 8- S -P(0.707 z< 2. 121) P( P(z2.121) P(z< -7.7) (diveusing excel) O 222822 o707 2.12 oo NoTmal probability bable then, you ant to use Plz 77)- P(z 2-121) o. 239783 - o.o1696 = o 222822 Nobe Narma pmbabiligy gives value for : p(z<-a) = P (z>a) = value bable Palabiliy

Merge & Center Font Alignment f NORMSDIST(2.121)-NORMSDIST(0.707) Formula Bar F E G 0.222822