Assume the random variable X is normally​ distributed, with mean μ=55 and standard deviation σ=4. Find the 11th percentile.

Answer 1

Find the z-stat corresponding to cumulative probability of 0.11, which will be 11th percentile, which is equal to -1.225.

Let x be value at 11th percentile.

Formula for z

z = (x - mean)/standard deviation

z for 11th percentile is -1.225. Mean and SD given as 55 and 4. Substitute values into equation to compute value of unknown x:

-1.225 = (x - 55)/4

x = 50.1.