IE 323 – Fall 2019

ASSIGNMENT #1

Remember…you are expected to do the textbook problems, but they do not have to be turned in.  Only turn in the answers to the questions below.

1. For each of the following, find the appropriate value for k and draw the corresponding graph (with the correct area under the curve shaded):

• P(-2.2 < Z < k) = 0.8943
  • P(Z > k) = 0.0392
  • P(Z < k) = 0.1736

• Using the T distribution, find the following and draw the corresponding graph (with the correct area under the curve shaded) :

• P(T > 2.101) when ν = 18.
• P(-0.856 < T < 2.787) when ν = 25.
• P(T < -1.833) when ν = 9.

• Using the χ² distribution, find the following and draw the corresponding graph (with the correct area under the curve shaded) :

• P(χ_α² < χ² < 22.307 ) = 0.875 when ν = 15
• P(χ² > χ_α²) = 0.025 when ν = 30.
• P(χ² < χ_α²) = 0.025 when ν = 30.

• For an F distribution, find the following and draw the corresponding graph (with the correct area under the curve shaded) :
•  
• P (F ³ f ) = 0.99 with n₁ = 8 and n₂ = 15. 
• P (F ³ f ) = 0.05 with n₁ = 7 and n₂ = 10. 
• f_0.95 (6, 10)
• P (F ³ 4.16) with n₁ = 12 and n₂ = 12.