Question: 26: Suppose that the random variable X is normally distributed with \(\mu =1000\) and \(\sigma =100\). Find the following probabilities:

(a) \(\Pr \left( 1000\le X\le 1200 \right)\)

(b) \(\Pr \left( X>1257 \right)\)

(c) \(\Pr \left( X<1035 \right)\)

(d) \(\Pr \left( 857\le X\le 1183 \right)\)

(e) \(\Pr \left( X\le 700 \right)\)

(f) \(\Pr \left( 812\le X\le 913 \right)\)

(g) \(\Pr \left( X>891 \right)\)

(h) \(\Pr \left( 1050\le X\le 1250 \right)\)