Question 1177765
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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.
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