SOLUTION: Let X ∼ N(10, 25). Compute (a) P(X ≤ 20) (b) P(X > 5) (c) P(12 ≤ X ≤ 15) (d) P(|X − 12| ≤ 15). Thank you

Algebra ->  Probability-and-statistics -> SOLUTION: Let X ∼ N(10, 25). Compute (a) P(X ≤ 20) (b) P(X > 5) (c) P(12 ≤ X ≤ 15) (d) P(|X − 12| ≤ 15). Thank you       Log On


   

Question 1177765: Let X ∼ N(10, 25). Compute
(a) P(X ≤ 20)
(b) P(X > 5)
(c) P(12 ≤ X ≤ 15)
(d) P(|X − 12| ≤ 15).
Thank you
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
Normal Distribution: N(10, 25) = N(μ, σ^2)  μ = 10   σ = 5
Using TI or similarly an inexpensive calculator like a Casio fx-115 ES plus
(a) P(X ≤ 20) = normalcdf(-9999, 20, 10, 5) = .9772
(b) P(X > 5) = 1 - P(x ≤ 5) = 1 - normalcdf(-9999, 5,10, 5) = 1 -.1587 = .8413
(c) P(12 ≤ X ≤ 15) =  normalcdf(12, 15, 10, 5) = .1859
(d) P(|X − 12| ≤ 15)  = P( x ≤ 27)  = .9997
P( x ≤ 27) includes P( x ≤ -3) 
Wish You the Best in your Studies.