Probability that a normal variate x lies in the range μ-3σ and μ is 0.4987.
How the area property of normal distribution works?
Area property of normal distribution as:
- P(μ-σ<x<μ+σ) = 0.6826
- P(μ-2σ<x<μ+2σ) = 0.9544
- P(μ-3σ<x<μ+3σ) = 0.9973
To find P(μ-3σ<x<μ)
P(μ-3σ<x<μ) = 1/2 P(μ-3σ<x<μ+3σ)
=1/2 × 0.9973
=0.4987
Hence, the value of P(μ-3σ<x<μ) is 0.4987
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