Question

7.5 we've established that heights of 10-year-old boys vary according to a Normal distribution with u = 138 cm and o = 7 cm a) What proportion of this population is less than 150 cm tall? b) What proportion is less than 140 cm in height? c) What proportion is between 150 and 140 cm?

Answer 1

- ut, x= height of so-year old boys. Y~ N(4,02) whore, H = 138 cm, D= 7 cm. . (a) PC*<150) = p/ * < 1407126) = P(Z<1171) = $(171) = 10.95617 than is less + 195 % of this population 150 cm. tall. 40-138 - (6) P(x<140) = P(Z < 1407136) = P(Z <0.29) = 10.29) = 10.6112 61.417 of this population in less than 140 cm lan C) Pl-140<x<150) = P(x<150) —P(72140) 0.9574 -0.6141 -0.34237 - 134.23% of this population is between 150 4140 en Scanned with CamScanner