Question

In a standard normal distribution, what z value corresponds to 17% of the data between the mean and the z value?

Answer 1

You're looking for a value $z$ such that

$\mathbb P(0$

Because the distribution is symmetric, the value of $z$ in either case will be the same.

Now, because the distribution is continuous, you have that

$0.17=\mathbb P(0$

The mean for the standard normal distribution is $0$, and because the distribution is symmetric about its mean, it follows that $\mathbb P(Z$.

$0.17=\mathbb P(Z$

You can consult a $z$ score table to find the corresponding score for this probability. It turns out to be $z\approx0.4399$.