Question

Assume the random variable X is normally distributed, with mean = 54 and standard deviation o = 8. Find the 15th percentile.

Answer 1

45.712

Explanation:

We need to find the Zscore of the area of 15 percent of the distribution ; using a Z table or calculator ;

Zscore of 15% of the distribution is : - 1.036

Using the Zscore formula :

Zscore = (x - mean) / standard deviation

Where, x = score

-1.036 = (x - 54) / 8

Cross multiply

-1.036 * 8 = x - 54

-1.288 = x - 54

x = - 8.288 + 54

x = 45.712