find z if the standard normal curve area between -z and z is 0.2013.
±0.215
±0.288
±0.315
±0.255

Question

Accepted Answer

# Explanation:
## Step1: Use the property of the standard normal curve
The area between $-z$ and $z$ is $A = 2\Phi(z)- 1$, where $\Phi(z)$ is the cumulative distribution function of the standard - normal distribution. Given $A=0.2013$, then $2\Phi(z)-1 = 0.2013$.
## Step2: Solve for $\Phi(z)$
$$
\begin{align*}
2\Phi(z)-1&=0.2013\
2\Phi(z)&=0.2013 + 1\
2\Phi(z)&=1.2013\
\Phi(z)&=\frac{1.2013}{2}\
\Phi(z)&=0.60065
\end{align*}
$$
## Step3: Look up the $z$ - value in the standard - normal table
Looking up the value $0.60065$ in the standard - normal table (z - table). The closest value to $0.60065$ in the standard - normal table corresponds to $z = 0.255$

# Answer:
$\pm0.255$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of the standard normal curve

Step2: Solve for \(\Phi(z)\)

Step3: Look up the \(z\) - value in the standard - normal table

Answer: