Question

Let z be the standard normal random variable. Find the z-score that has 26.11% of the distribution’s area to its left.

Answer 1

Z is the standard normal random variable.

We have to find the z-score, which has 26.11% of the distribution's area to it's left.

Now, this actually implies, we have to find the value of z, such that

ie. we have to find the value of z, such that

Now, to find z value, we have to consult the standard normal table.

Now, we know that the distribution function of the standard normal variate Z, is given by the phi function.

So,

this actually implies

.....(i)

From the standard normal table, we find that

.....(ii)

So, comparing (i) and (ii), we can say that

So, the z-score that has 26.11% of the distribution's area to it's left, is -0.64.