X is a normally distributed random variable with a standard deviation of 2.00. Find the mean of X if 12.71% of the area under the distribution curve lies to the right of 8.28. (Note: the diagram is not necessarily to scale.)
A) 7.6
B) 6.6
C) 6.0
D) 5.5

Question

X is a normally distributed random variable with a standard deviation of 2.00. Find the mean of X if 12.71% of the area under the distribution curve lies to the right of 8.28. (Note: the diagram is not necessarily to scale.) 
A) 7.6 
B) 6.6 
C) 6.0 
D) 5.5

Quizplus · Accepted Answer

12.71% of the area under the curve lies to the right of 8.28. Therefore, 87.29% of the area lies to the left of $8.28$.
From the z-table, we find that the z-score corresponding to the 87.29th percentile is $z=1.15$ (approximately).
Therefore, $$8.28 = \mu + 1.15(2)$$
Solving for $\mu$, we get $\mu = 6.0$.

X Is a Normally Distributed Random Variable with a Standard