Question

what is the 10th percentile of the standard normal distribution? -1.28 1.28 0.9 -0.90

Explanation:

Step1: Recall the definition of percentile in standard normal distribution

The \(p\) - th percentile of a standard normal distribution \(Z\sim N(0,1)\) is a value \(z_p\) such that \(P(Z\leq z_p)=p/100\).
For the \(10^{th}\) percentile, we want to find \(z\) such that \(P(Z\leq z) = 0.10\).

Step2: Use the standard normal table (z - table)

Looking up the value in the standard normal table (the cumulative distribution function of the standard normal distribution \(\varPhi(z)=P(Z\leq z)\)).
We know that \(\varPhi(- 1.28)\approx0.1003\) and \(\varPhi(-0.90)\approx0.1841\).

Answer:

-1.28