Question

question 7
given a standardized normal distribution, what is the value of z if only 2.5 percent of all possible z values are larger?
+1.96
-1.96
+-1.96

Explanation:

Step1: Analyze the problem

We are dealing with a standardized normal distribution ($Z$-distribution). The total area under the standard normal curve is $1$. If only $2.5\%$ (or $0.025$) of all possible $Z$ values are larger, we need to find the $Z$ - score such that $P(Z>z)=0.025$.
Since $P(Z > z)=0.025$, then $P(Z\leq z)=1 - 0.025=0.975$ (using the property that $P(Z\leq z)+P(Z > z)=1$ for any real - valued $z$).

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

The standard normal table gives the cumulative probability $P(Z\leq z)$. Looking up the value $0.975$ in the body of the standard normal table (the $z$ - table).
The standard normal table is symmetric about $z = 0$. The $z$ - score corresponding to a cumulative probability of $0.975$ is $z = 1.96$.

Answer:

+1.96