Respuesta :
The formula for z-score is given as
[tex]z=\frac{x-\mu}{\sigma}[/tex]we will have to calculate two values of the z-scores
The given values are
[tex]\begin{gathered} x_1=\text{ \$877} \\ \mu_1=\text{ \$982} \\ \sigma_1=\text{ \$180} \end{gathered}[/tex]By substitution, we will have
[tex]\begin{gathered} z_1=\text{ }\frac{\text{\$877- \$982}}{\text{ \$180}} \\ z_1=\text{ }\frac{\text{-\$105}}{\text{ \$180}} \\ z_1=-\text{ 0.5833} \end{gathered}[/tex]we will then calculate the second z-score
The given values are
[tex]\begin{gathered} x_2=\text{ \$1042} \\ \sigma_2=\text{ \$180} \\ \mu_2=\text{ \$982} \end{gathered}[/tex]By substitution, we will have
[tex]\begin{gathered} z_2=\frac{\text{ \$1042 - \$982}}{\text{ \$180}} \\ z_2=\text{ }\frac{\text{60}}{180} \\ z_2=0.3333 \end{gathered}[/tex]P(-0.5833 ≤ z ≤ 0.3333) = 0.3507
Hence the probability that a randomly selected mortgage payment is between $877 and $1,042 is 0.3507
