dispersion

(a) Mean = 107.
(b) P(107 < X < 129) = 950/2000 = 0.475
P[(107 - 107)/s < (X - 107)/s < (129 - 107)/s] = 0.475
P(0 < Z < 22/s) = 0.475
From the table, A(22/s) = A(1.96)
so 22/s = 1.96, s = standard deviation = 22/1.96 = 11.2245
(c)
P(genius) = P(X > 140) = P[(X - 107)/11.2245 > (140 - 107)/11.2245]
= P( Z > 2.94) = 1 - 0.5 - A(2.94)
A(2.94) = 0.4984
so P(genius) = 1 - 0.5 - 0.4984 = 0.0016
No. of genius = 2000 x 0.0016 = 3.2