Question

Topic: Normal Distribution Distribution & Inverse Normal Distribution

1. Given that  X~N (4,9), find

a.) P(X > 8)

b.) P(4< X < 6)

c.) P(X≥3)

Answer 1

Given $N(4, 3^2):\mu=4, \sigma=3$

a,

$$P(X>9)=1-P(X\leq 9)=$$

$$\approx1-P(Z\leq \dfrac{9-4}{3})\approx1-P(Z\leq 1.666667)$$

$$\approx0.047790$$

b,

$$P(4<X<6)=P(X<6)-P(X\leq 4)=$$

$$\approx P(Z< \dfrac{6-4}{3})-P(Z\leq \dfrac{4-4}{3})$$

$$\approx P(Z\leq 0.666667)-P(Z\leq 0)$$

$$\approx0.747507-0.5\approx0.247507$$

c,

$$P(X\geq3)=1-P(X<3)=$$

$$\approx1-P(Z< \dfrac{3-4}{3})\approx1-P(Z\leq -0.333333)$$

$$\approx0.630559$$