Q. 6.27 - Elementary Statistics

Question

The area under a particular normal curve to the left of 105 is 0.6227. A normally distributed variable has the same mean and standard deviation as the parameters for this normal curve. What percentage of all possible observations of the variable lie to the Ieft of 105? Explain your answer. 

Step-by-Step Solution

Answer

$62.27\%$ of all possible observations of the variable lie to the Ieft of 105.

Step 1. Given Information.

The area under a particular normal curve to the left of 105 is 0.6227. 

Step 2. Find the percentage.

A normally distributed variable has the same mean and standard deviation as the parameters for this normal curve.  

For a normally distributed variable, the value of all possible observations that lie within any specified range equals the corresponding area under its associated normal curve expresssed as percentage. 

So the percentage is $62.27\%$