In each case, determine the value of the constant c that makes the probability statement correct.

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$P(c \le |Z|)=0.016$

Here is my attempt:

$P(|Z| \ge c)=0.016$

$P(Z \ge c~or~Z \le -c) = 0.016 $

$<1-\phi (c)> - \phi (-c) = 0.016$

By symmetry, $1-\phi (c)$ and $\phi (-c)$ are equal.

$2 \phi (-c) = 0.016 \implies \phi (-c) = 0.008$.

However, this doesn"t lead to the correct solution. What exactly did I solve for? And how was I actually suppose to solve this question?


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You started correctly: We want a combined probability of $0.016$ in the two tails $Z\ge c$ and $Z\le -c$. By symmetry, we want a probability of $\frac{0.016}{2}=0.008$ in the "right tail."

Equivalently, we want $\Pr(Z\le c)=1-0.008=0.992$. Look for $0.9992$ in the body of your standard normal table.


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