Q. 6.28 - Elementary Statistics

Question

The area under a particular normal curve between $10$ and $15$ is $0.6874$. 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 between $10$ and $15$? Explain your answer.

Step-by-Step Solution

Answer

If the area under the normal curve lies between 10, 15  is 0.6874, then $68.74\%$ of all possible observation of the variable lies between 10, 15.

Step 1. Given Information.

The area under a particular normal curve between $10$ and $15$ is $0.6874$.

Step 2. Find the percentage.

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.

If the area under the normal curve lies between 10, 15  is 0.6874, then $68.74\%$ of all possible observation of the variable lies between 10, 15.