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Q) Let $x$ be normal variable with mean $8$ and standard deviation $4$ then $p(X\leq5)$ is

A). Greater than zero but less than $0.5$

B). Greater than $0.75$

C). Greater than $0.5$ but less than $1$

D). Equal to $0.5$

A is correct.

I think the right option is A.

This is the normal distribution curve for this mean and standard deviation μ=8 and σ=4

Since the area under the curve from μ-3σ(-4 here) to μ(8) is 0.5 hence P(x≤5) will be even smaller but will not be zero. Hence option A is correct.

P(x<=5)= (5-8)/4= -3/4= -0.75

probability cant be negative= B is ans