Assume the random variable X is normally​ distributed, with mean 60 and standard deviation 5 . Find the 6th percentile.

Answer 1

Hi Gabriel,

This is a variation on the classic equation in introductory statistics:

z=x-mu/sigma.

Now, you were given a percentile, which is the equivalent of a probability. SInce your data is normally distributed, we can do a “reverse lookup” on the z-table. You were given the sixth percentile—this equates to 0.06. Look on the z-table for this value.

z_0.06= -1.555

Now, let’s break down:

z=(x-mu)/sigma

z= -1.555

mu=mean

sigma=standard deviation

x=value we are looking for

For this problem:

Z= -1.555

mu=60

sigma=5

x=x

Substituting:

-1.555=(x-60)/5

Multiply both sides by 5:

-7.775=x-60

Add 60:

x=52.225

I hope this helps.