#1.
Here, μ = 2.5, σ = 0.01 and x = 2. We need to compute P(X <= 2).
The corresponding z-value is calculated using Central Limit
Theorem
z = (x - μ)/σ
z = (2 - 2.5)/0.01 = -50
Therefore,
P(X <= 2) = P(z <= (2 - 2.5)/0.01)
= P(z <= -50)
= 0
#2.
Here, μ = 105, σ = 20/sqrt(20) = 4.4721, x1 = 102 and x2 = 110. We
need to compute P(102<= X <= 110). The corresponding z-value
is calculated using Central Limit Theorem
z = (x - μ)/σ
z1 = (102 - 105)/4.4721 = -0.67
z2 = (110 - 105)/4.4721 = 1.12
Therefore, we get
P(102 <= X <= 110) = P((110 - 105)/4.4721) <= z <= (110
- 105)/4.4721)
= P(-0.67 <= z <= 1.12) = P(z <= 1.12) - P(z <=
-0.67)
= 0.87 - 0.25
= 0.62
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