In each instance, identify the value of the consistent c that provides the probcapability statement correct.

You are watching: In each case, determine the value of the constant c that makes the probability statement correct

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

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 also $phi (-c)$ are equal.

$2 phi (-c) = 0.016 indicates phi (-c) = 0.008$.

However before, this doesn"t bring about the correct solution. What exactly did I deal with for? And just how was I actually expect to solve this question?


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You began correctly: We want an unified probability of $0.016$ in the two tails $Zge c$ and also $Zle -c$. By symmetry, we want a probability of $frac0.0162=0.008$ in the "appropriate tail."

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


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