Given:
[tex]\mu=218.4,\sigma=86.3.n=167\text{ and M=220.4}[/tex]The z-score value is
[tex]z=\frac{M-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex][tex]\text{Substitute }\mu=218.4,\sigma=86.3.n=167\text{ and M=220.4, we get}[/tex][tex]z=\frac{220.4-218.4}{\frac{86.3}{\sqrt[]{167}}}[/tex][tex]z=\frac{\sqrt[]{167}(220.4-218.4)}{86.3}[/tex][tex]z=0.29949[/tex]The P-value from the z-table is
[tex]P(218.4[tex]P(M<220.4)=0.11772+0.5[/tex][tex]P(M<220.4)=0.61772[/tex]Hence the answer is
[tex]P(M<220.4)=0.61772[/tex]