Question

The height of an adult male is known to be normally distributed with mean of 175 cm and standard deviation of 6 cm. The 20th percentile (bottom 20%) of the distribution of heights is shorter than:

Answer 1

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

$Z=\frac{X-\bar{X }}{\sigma }\\\\\Rightarrow -0.84166=\frac{X-175}{6}\\\\\therefore X=-0.84166\times 6+175\\\\X=169.95cm$