Suppose the heights of women at a college are approximately Normally distributed with a mean of 65 inches and a population standard deviation of 2.5 inches. What height is at the 20 th percentile? Include an appropriately labeled sketch of the Normal curve to support your answer.
Accepted Solution
A:
Answer:The height that is at the 20th percentile is 62.9 in.Step-by-step explanation:A percentile indicates the value which a given percentage of observations in a group of observations falls.The 20th percentile is the value below which 20% of the observations may be found.In this case, we have a normal distribution with mean of 65 in. and standard deviation of 2.5 in. We can use the standarized z-table to find the value of z for the 20th percentile. The value of z for the 20th percentile is z=-0.842.We can transform this to the normal distribution of this model ([tex]N(65,2.5^2)[/tex]):[tex]x=\mu+z*\sigma=65+(-0.842)*2.5=62.9[/tex]The height that is at the 20th percentile is 62.9 in.In the picture we can see the percentage that falls below this value (20%).