Question

suppose the weights of filipino grade 11 students are normally distributed with a mean of 52 kilograms and a standard deviation of a kilogram.​

Answer 1

Step-by-step explanation:

Here μ=51 and σ=15

Z=

σ

X−μ

=

15

X−151

When X=120, Z=

15

120−151

=−2.067

When X=155, Z=

15

155−151

=0.2667

When X=185, Z=

15

185−151

=

15

35

=2.2667

(i) P(120<X<155)=P(−2.07<Z<0.27)

=∫

−2.067

0.2667

ϕ(z)dz=∫

0

0.2667

ϕ(z)dz+∫

0

2.0667

ϕ(z)dz

=0.4803+0.1026=0.5829.

Here N=500

∴ The number of students whose weight is between 120 and 155 pounds is

0.5872×500=291

(ii) P(X<185)=P(Z>2.27)=∫

2.2667

∞

ϕ(z)dz

=∫

0

∞

ϕ(z)dz−∫

0

2.2667

ϕ(z)dz=0.5−0.4881=0.0119