please be very specific on showing work done!! If Z∼N(μ=0,σ2=1)Z∼N(μ=0,σ2=1), find the following probabilities: P(Z<1.58)=P(Z<1.58)= P(Z=1.58)=P(Z=1.58)=...

please be very specific on showing work done!!

If Z∼N(μ=0,σ2=1)Z∼N(μ=0,σ2=1), find the following probabilities:

P(Z<1.58)=P(Z<1.58)=
P(Z=1.58)=P(Z=1.58)=
P(Z>−.27)=P(Z>−.27)=
P(−1.97<Z<2.46)=

Expert Solution

Z~N(0,1)

P(Z<1.58)=0.9429

P(Z=1.58)=0 as for continuous distribution exact probability is equal to zero

P(Z>-0.27)=1-P(Z<-0.27)=1-0.3936=0.6064

P(-1.97 <Z<2.46)=P(Z<2.46)-P(Z<-1.97)=0.9930-0.0244=0.9686

PFA normal table for reference

milcah answered 1 year ago

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