please explain 5 6 8 Find the area of the shaded region The

please explain #5, 6, 8

Find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a slandered deviation of 15 (as on the Wechsler test).

Solution

X~N(100, 225)

Mean=100, std. dev=15 so, var=225

Let Z= (X-100) / 15 then clearly, Z~N(0,1)

(5) P(X<118)=P(Z<18/15)=P(Z<1.2)=0.8849303

(6) P(X>91)=P(Z> -9/15) =1-P(Z<= -3/5)= 0.7257469

(7) P(79<X<133)=P((79-100)/15<Z<(133-100)/15)=P(-21/15<Z<33/15)=0.9053399

(8) P(112<X<124)=P(12/15<Z<24/15)=0.1570561