Answer
0.0753
Step-by-step explanation
First, we need to compute the z-scores of the situations.
z-score is calculated with the next formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where
• x: observed value
,• μ: mean
,• σ: standard deviation
Substituting μ = $580, σ = $125, x = $400, in one case, and x = $1000, in the other case, we get:
[tex]\begin{gathered} z_1=\frac{400-580}{125}=-1.44 \\ z_2=\frac{1000-580}{125}=3.36 \end{gathered}[/tex]The probability a random person from Superior has less than $400 or more than $1000 in their bank account is calculated as follows:
[tex]P(z\lt-1.44\text{ or }z\gt3.36)=P(z\lt-1.44)+P(z\gt3.36)[/tex]From the above table:
[tex]P(z\lt-1.44)=0.0749[/tex]From the above table:
[tex]P(z\gt3.36)=1-0.9996=0.0004[/tex]Substituting these results into the formula:
[tex]\begin{gathered} P(z\lt-1.44\text{ or }z\gt3.36)=0.0749+0.0004 \\ P(z\lt-1.44\text{ or }z\gt3.36)=0.0753 \end{gathered}[/tex]
