If Z~N(0,1) find

P[Z<-2]

P[-2<Z<0]

P[Z>2]

P[Z<2]

actually i just dont know the category ..sorry :p
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1 Answer

This looks like a normal distribution bell-curve with μ (mean)=0 and σ (standard deviation)=1.

Z is usually calculated from Z=(X-μ)/σ=X in this case. So Z<-2 is equivalent to a datum X=-2.

Normal distribution tables give the probability associated with Z-scores (the area underneath the bell-curve to the left of the Z-score). Z=-2 means 2 standard deviations below the mean.

P[Z<-2]=0.02275 or 2.275%;

P[Z<0]=0.5 or 50% (half the results (area) are below 0 and half above), so:

P[-2<Z<0]=P[Z<0]-P[Z<-2]=0.5-0.02275=0.47725 or 47.725%;

P[Z>2]=P[Z<-2]=0.02275 because of symmetry: the area above Z=2 is the same size as the area below Z=-2;

P[Z<2]=1-0.02275=0.97725 because the area under the bell-curve is 1 (100% probability).

by Top Rated User (1.2m points)

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