Suppose that Xi are IID normal random variables with mean 2 and variance 1, for i...

Question

Question

Suppose that Xi are IID normal random variables with mean 2 and variance 1, for i = 1, 2, ..., n. (a) Calculate P(X1 < 2.6),

Answer 1

Answer #1

a)

for normal distribution z score =(X-μ)/σx

here mean= μ=	2
std deviation =σ=	1.000

probability =P(X<2.6)=(Z<(2.6-2)/1)=P(Z<0.6)=0.7257

b)

sample size =n=	2
std error=σ_x̅=σ/√n=	0.70711

probability =P(X>3)=P(Z>(3-2)/0.707)=P(Z>1.41)=1-P(Z<1.41)=1-0.9207=0.0793

c)

probability =P(X>2.7)=P(Z>(2.7-2)/0.707)=P(Z>0.99)=1-P(Z<0.99)=1-0.8389=0.1611

d)

sample size =n=	100
std error=σ_x̅=σ/√n=	0.10000

probability =P(1.85<X<16.1)=P((1.85-2)/0.1)<Z<(16.1-2)/0.1)=P(-1.5<Z<141)=1-0.0668=0.9332

Answer 2

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