Question

If x is normally distributed random variable with a mean of 8.20 and variance of 4.41, and that p(x >

b.= .08, then the value of b is:

Answer 1

Given that mean is 8.20 and variance is 4.41, the value of b will be calculated as follows:
P(x>b)=0.08
⇒P(x<b)=1-0.08=0.92
the z-score corresponding to this probability is:
z=1.41
but the formula for z-score is given by:
z=(x-μ)/σ
where:
μ=mean
σ=standard deviation
thus plugging in the values we obtain:
1.41=(x-8.2)/√4.41
1.41=(x-8.2)/2.1
solving for x
1.41×2.1=x-8.2
x=2.961+8.2
x=11.161

Hence the answer is x=11.161