Given:
[tex]Mean\text{ }\mu\text{ =4.5, standard deviation }\sigma\text{ =0.8, and x =4.}[/tex]Required:
We need to find the percentage of the time will the police take 4 minutes or less to arrive.
Explanation:
Consider the z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]Substitute\text{ }\mu\text{ =4.5, }\sigma\text{ =0.8, and x =4 in the formula.}[/tex][tex]z=\frac{4-4.5}{0.8}[/tex][tex]z=-0.625[/tex]P-value from Z-Table
[tex]P(x<4)=0.26599[/tex]Multiply by 100 to find the percentage.
[tex]P(x<4)\text{ \%}=0.26599\times100[/tex][tex]P(x<4)\text{ \%}=26.599\text{ \%}[/tex][tex]P(x<4)\text{ \%}=27\text{ \%}[/tex]Final answer:
27 % of the time will the police take 4 minutes or less to arrive.
