Work done so far.... If X ~ N(22,4), z = (x - 22)/sqrt(4) ~ N(0,1) Thus, P(20 <= X <= 21) = P((22-20)/2 <= z <= (22-21)/2) = P(1<= z <= 0.5) = P(z <= 1) - P(Z <= 0.5) Now, we use the table above. P(z <= 1) - P(Z <= 0.5) = 0.8413-0.6915=0.1463
Is it correct?
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Check your arithmetic at the very end, using numeric integration (assuming and I'm not familiar with the notation given) I find:
and using the table I have, I get 0.1498
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