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.

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