Assume that Y is normally distributed N(μ,σ2).To find Pr(c1 ≤ Y ≤ c2),where c1

Question

Assume that Y is normally distributed N(μ,σ2).To find Pr(c1 ≤ Y ≤ c2),where c1 < c2 and di =  ,you need to calculate Pr(d1 ≤ Z ≤ d2)=
A)Φ(d2)- Φ(d1) 
B)Φ(1.96)- Φ(1.96) 
C)Φ(d2)- (1 - Φ(d1)) 
D)1 - (Φ(d2)- Φ(d1))

Quizplus · Accepted Answer

To find Pr(c1 ≤ Y ≤ c2),
we standardize the equation by subtracting μ from both bounds and dividing by σ:
Pr(c1 ≤ Y ≤ c2) = Pr((c1-μ)/σ ≤ (Y-μ)/σ ≤ (c2-μ)/σ)
Let Z = (Y-μ)/σ, then Z is a standard normal random variable.
Thus, Pr(c1 ≤ Y ≤ c2) = Pr((c1-μ)/σ ≤ Z ≤ (c2-μ)/σ) = Pr(d1 ≤ Z ≤ d2).
Therefore, the probability can be calculated using the standard normal table as Φ(d2)- Φ(d1). So, the answer is A.

Assume That Y Is Normally Distributed N(μ,σ2)