Question

Cholesterol level has a Normal distribution N(170,30), find the first quartile.

Answer 1

Step-by-step explanation:

In statistics, the quartile is a measurement of the spread of values within a dataset above and below the mean via a division of the distribution into four defined intervals. A quartile partitions the data at three points within the distribution.

• 25% of the data lies below the lower or first quartile, denoted as $Q_{1}$.

• 50% of the data lies below the median or second quartile, denoted as $Q_{2}$.

• 75% of the data lies below the upper or third quartile, denoted as $Q_{3}$.

Thus, logically, we know that the remaining 25% of the data lies above the third quartile.

As shown in the figure below, the score that defines the first quartile of the defined normal distribution is the same as the score that, when evaluated in the cumulative density function, $\Phi$, gives 25% of the area under the bell curve.

To find this z-score, we can use the help of the NORM.INV function in Microsoft Excel, which obtains the inverse of the normal cumulative distribution and the syntax, type into a cell, is as follows:

                                     $=\text{NORM.INV(0.25, 170, 30)}$

which gives you the value 149.77  (2 s.f.).

This means that 25% of the values of cholesterol levels lie below 149.77.