Question

X is a normally distributed random variable with a mean of 11 and a standard deviation of 2.0. find the value of x for which 70.54% of the area under the distribution curve lies to the right of it. (note: the diagram is not necessarily to scale.

Answer 1

For the random variable x, the z-score is
z = (x - 11)/2

Because 70.54% of the area under the curve lies to the right of x, therefore the area to the left of x is
100 - 70.54 = 29.46%

From the standard table, a z-score of -0.54 will yield an area of 29.46% to the left of x.
Therefore
(x - 11)/2 = -0.54
x - 11 = -0.54*2
x = 9.92

Answer: 9.92