Academic Master

Mathematics

Mathematical Questions

1)

Let X denote IQ of an individual. Then  X\sim N(\mu=100,\sigma^{2}=15^{2})

a)

P(X>138)=P(Z>\frac{138-100}{15})=P(Z>2.53)=1-P(Z<2.53)

=1-0.9943=0.0057  i.e. 0.57%

b)

P(X>150)=P(Z>\frac{150-100}{15})=P(Z>3.33)=1-P(Z<3.33)

=1-0.99957=0.00043  i.e. 0.043%

Required number of students = 0.00043(12000) = 5.16 ~ 5

c)

P(X<70)=P(Z<\frac{70-100}{15})=P(Z<-2)=P(Z>2)

=1-P(Z<2)=1-0.97725=0.02275  i.e. 2.275%

d)

We want to find ‘x’ such that  P(X>x)=0.01

P(Z>\frac{x-100}{15})=0.01

From Normal probability tables, we get

\frac{x-100}{15}=2.3263\Rightarrow x=134.8945\sim 135  which is the required IQ.

Q2.

a) z = (3 – 5.2)/1.3

z = – 0.733

P = 0.2327

b) z = (2 – 5.2)/1.3

z = – 2.46

P = 0.006947

Get back = 150000 * 0.006947

Get back = about 1042

c) z score for lowest 10% = – 1.28

(x – 5.2)/1.3 = – 1.28

x = 3.536

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