Question

which z-values correspond to the middle 20% of the standard normal distribution? round your answers to the nearest thousandth. < z <

Explanation:

Step1: Calculate the area in the tails

The total area under the standard normal curve is \(1\). If the middle area is \(0.20\), then the area in the two tails is \(1 - 0.20=0.80\). The area in each tail is \(\frac{0.80}{2}=0.40\)

Step2: Find the \(z\) - value for the left - hand tail

We want to find \(z_1\) such that \(P(Z < z_1)=0.40\). Using a standard normal table (or a calculator with a normal - distribution function, e.g., the invNorm function on a TI - 84: invNorm\((0.40,0,1)\))

$$z_1\approx - 0.253$$

Step3: Find the \(z\) - value for the right - hand tail

Since the standard normal distribution is symmetric about \(z = 0\), if \(z_1\) is the \(z\) - value for the left - hand tail, then the \(z\) - value for the right - hand tail \(z_2=-z_1\)

$$z_2\approx0.253$$

Answer:

\(-0.253