what is the cut off height for the shortest 20% of babies with an average of 65cm and standard deviation of 10cm

Question

Please show the steps so I can understand how to solve the problem

Answer 1

Rihannon:

 

Assume that the heights of babies, denoted by X, are NORMALLY distributed with mean 65 cm and SD 10cm. 

 

Let x* denote the cut-off height for the shortest 20% babies.  You want to know how to fund x*.

 

Step 1: Convert x* to a "z_value" gieven by z = (individual value - mean) / SD = (x* -65)/10.

 

Step 2: Get z from the normal tables in your text (or from your calculator, or from the internet, wherever, see below) such that to the left that z ( that is from -infinity to that z) the area under the STANDARD NORMAL curve (mean 0, SD 1) is 20%

 

If you do not have a table or a calculator that gives this z, go to the internet and open the free website

 

http://stattrek.com/online-calculator/normal.aspx

 

Enter in the box in front of cumulative probability, 0.2, in front of mean, 0, and in front of syandard deviation,  1, and press calculate.  You should get z = -0.842.

 

Step 3: Go to Step 1, set -0.842 = (x* - 65)/10 and solve for x*.  You should get x* = 56.584.

 

The cut-off height for the shortest 20% babies in the given question assuming normal distribution of heights of babies, is 56.684.

 

 

Dr. G.

 

P.S. You COULD input 02, 65 and 10 in that order on the screen of the website, but I wanted you to know how to find it in case you just want to use standard normal tables from a book.