Question

X-N(12,16)

P(X<a)=0.1

Solve for a

Answer 1

I'm guessing this is a statistics question where N(μ,σ²) is the normal distribution for a mean μ and variance σ². The standard deviation σ is the square root of variance. Given that μ=12 and σ²=16, σ=√16=4.

The Z-score is (a-12)/4. From tables Z=-1.28155 approx for a probability of 0.1.

So (a-12)/4=-1.28155, a-12=-5.1266, a=6.8738 approx. a=6.87 to 2 decimal places.

This satisfies P(X<6.87)=0.1.