Questions: Suppose (Z) follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of (c) so that the following is true. [ P(Z>c)=0.1357 ] Round your answer to two decimal places.

Suppose (Z) follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of (c) so that the following is true. [ P(Z>c)=0.1357 ] Round your answer to two decimal places.
Transcript text: Suppose $Z$ follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of $c$ so that the following is true. \[ P(Z>c)=0.1357 \] Round your answer to two decimal places. $\square$
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Solution

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Solution Steps

Step 1: Understand the problem

We are given that \( Z \) follows the standard normal distribution, and we need to find the value of \( c \) such that \( P(Z > c) = 0.1357 \). This means we are looking for the value of \( c \) where the probability of \( Z \) being greater than \( c \) is 0.1357.

Step 2: Use the standard normal table or calculator

Since \( P(Z > c) = 0.1357 \), we can rewrite this as \( P(Z \leq c) = 1 - 0.1357 = 0.8643 \). We now need to find the value of \( c \) such that the cumulative probability up to \( c \) is 0.8643.

Using a standard normal table or calculator, we look for the value of \( c \) that corresponds to a cumulative probability of 0.8643.

Step 3: Find the value of \( c \)

From the standard normal table or calculator, we find that the value of \( c \) corresponding to a cumulative probability of 0.8643 is approximately \( c = 1.10 \).

Final Answer

\[ \boxed{c = 1.10} \]

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