I'm struggling to solve these probabilty equations, please help
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The table gives 0.5714 for Z<0.18 and 0.3707 for Z<-0.33, so if we subtract these two values we get Z between -0.33 and 0.18: 0.2007.

Similarly 0.6480 for Z<0.38 and 0.9236 for Z<1.43, the probability (area)=0.9236-0.6480=0.2756.

It's a lot easier when you have a picture of the normal distribution curve. The probabilities for Z values are areas under the curve. Z=0 is the vertex of the curve, the highest point, representing the mean. The probability quoted in tables are the areas to the left of the Z value. So, to find the probability in a range you need to subtract areas. Also, the table is symmetrical so if you only have probabilities for Z>0 you can find negative Z by subtracting from 1 because the total probability or area under the curve is 1. So P(-Z)=1-P(Z). Hence P(-0.33)=1-P(0.33)=1-0.6293=0.3707.

by Top Rated User (1.2m points)

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