Probability Statistics question, a bit confused.

Question

A population of snakes have total lengths: 7cm, 5cm, 10cm, 13cm, and 9cm.

 

If two snakes are selected at random without replacement (order does not matter), what is the probability that the sample mean will be within 1 standard error of the population mean

Answer 1

This is a solid Statistics problem, as it combines knowledge of Sampling Distributions and Normal/Density Curves. I'm assuming that you have a TI-84 calculator, as I teach AP Statistics and we streamline things with the calculator. Step 1: enter the five lengths into your table by using STAT button and going to Edit. Step 2: Use STAT button, move to CALC, hit 1 Var Stats, ensure your List match the data that was entered, and go to calculate. Step 3: Take the mean of 8.8 and the S_x of 3.033 to calcuate the SE. SE equals 3.033/√5, which is 1.356. Step 4: Take 8.8 plus OR minus the SE, which is 8.8 plus OR minus 1.356. Step 5: The lower boundary is 7.444 and the upper boundary is 10.156. From here, you can calculate the Z-score for the two boundaries or simply use the normalcdf function in.....Step 6: Use 2nd VARS, go to normalcdf (7.444, 10.156, 8.8, 3.033) and get the probability of .3452 or 34.52%.