Answer:
The height below which 20% of the persons lie equals 169.95 cm
Step-by-step explanation:
Given that
Mean height = 175 cm
Standard deviation = 6 cm
Hence for the given question we need to find the standard variate factor ( Z factor) corresponding to the 20% of the area under the standard normal distribution curve
Using the standard normal distribution tables we have Z factor corresponding to an area of 20% equals ( Z = -0.84166)
Thus we have
[tex]Z=\frac{X-\bar{X }}{\sigma }\\\\\Rightarrow -0.84166=\frac{X-175}{6}\\\\\therefore X=-0.84166\times 6+175\\\\X=169.95cm[/tex]
