Answer:
The percentage of the distribution is less than 75 is 97.72%.
Step-by-step explanation:
Given,
Mean of the distribution,
[tex]\mu=67[/tex]
Standard deviation,
[tex]\sigma = 4[/tex]
Thus, the z-score of the score 75,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]=\frac{75-67}{4}[/tex]
[tex]=\frac{8}{4}[/tex]
[tex]=2[/tex]
With the help of z-score table,
[tex]P(x<75)=0.9772=97.72\%[/tex]
Hence, the percentage of the distribution is less than 75 is 97.72%.