Answer to Question #280683 in Statistics and Probability for Jack

Question

L + x be a nœemal randome variable with mean 4 and variouse dot alpha Find the probability 8li * e_{s}

1) Between 4 and 6

2) Between 5 and 7.5

3) ・2 and 3.

4) greater them d * 75

5) Less than 4.025.

Answer 1

mean:

$\mu=4$

standard deviation:

$\sigma=8$

$z=\frac{x-\mu}{\sigma}$

1)

$z_1=\frac{4-4}{8}=0$

$z_2=\frac{6-4}{8}=0.25$

$P(4<x<6)=P(z_1<z<z_2)=0.5987-0.5=0.987$

2)

$z_1=\frac{5-4}{8}=0.125$

$z_2=\frac{7.5-4}{8}=0.44$

$P(7.5<x<5)=P(z_1<z<z_2)=0.67-0.5478=0.1222$

3)

$z_1=\frac{2-4}{8}=-0.25$

$z_2=\frac{3-4}{8}=-0.125$

$P(2<x<3)=P(z_1<z<z_2)=0.4522-0.4013=0.0509$

4)

$z=\frac{7.5-4}{8}=0.44$

$P(x>7.5)=P(z>0.44)=1-0.67=0.33$

5)

$z=\frac{4.025-4}{8}=0.003$

$P(x<4.025)=P(z<0.003)=0.5$