Question #217724

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)



1
Expert's answer
2021-07-19T05:52:20-0400

Given N(4,32):μ=4,σ=3N(4, 3^2):\mu=4, \sigma=3


a,


P(X>9)=1P(X9)=P(X>9)=1-P(X\leq 9)=

1P(Z943)1P(Z1.666667)\approx1-P(Z\leq \dfrac{9-4}{3})\approx1-P(Z\leq 1.666667)

0.047790\approx0.047790

b,


P(4<X<6)=P(X<6)P(X4)=P(4<X<6)=P(X<6)-P(X\leq 4)=

P(Z<643)P(Z443)\approx P(Z< \dfrac{6-4}{3})-P(Z\leq \dfrac{4-4}{3})

P(Z0.666667)P(Z0)\approx P(Z\leq 0.666667)-P(Z\leq 0)

0.7475070.50.247507\approx0.747507-0.5\approx0.247507

c,


P(X3)=1P(X<3)=P(X\geq3)=1-P(X<3)=

1P(Z<343)1P(Z0.333333)\approx1-P(Z< \dfrac{3-4}{3})\approx1-P(Z\leq -0.333333)

0.630559\approx0.630559


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS