I'm trying to solve (i), I keep on finding that the answer to the question is 0.72. Nonetheless correct answer is shown to be 0.288.
My workings: $$P(\frac{-0.5}{1.4}<Z<\frac{0.5}{1.4}) = P(-0.357<Z<0.357)$$ Based on the Standard Normal distribution table (Right tail only) we have: $$0.36 = 0.1406$$ I then proceed to get the area under both tails: $$ 0.1406 * 2 = 0.28$$ and substract that value from 1 in order to get the area in the middle ( between 0 and 1 ): $$ 1-0.28 = 0.72$$
Could someone possible tell me why we should substract the value from 1 at the end? Thank you very much in advance
I suspect that based on the table you find something like:$$P(Z\geq0.36)\approx0.1406$$Taking that twice gives: $$P(Z\leq-0.36\text{ or }Z\geq0.36)=P(Z\leq-0.36)+P(Z\geq0.36)=2P(Z\geq0.36)\approx0.28$$Then:$$P(-0.36<Z<0.36)=1-P(Z\leq-0.36\text{ or }Z\geq0.36)\approx0.72$$