Question

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.

• μ = 1000 FTES

• median = 1,014 FTES

• σ = 474 FTES

• first quartile = 528.5 FTES

• third quartile = 1,447.5 FTES

• n = 29 years

75% of all years have an FTES:

a. at or below: _____

b. at or above: _____

Short answer

75% of all years have an FTES:

a. At or below 1447.5

b. At or above 528.5

Step-by-step solution

To find

75 % of all years have an FTES:

a. At or below

b. At or above

Explanation

The median is a number that splits the data into two equal halves and is one of the measures of central tendency in statistics. The data in the 50% range is below the median value while the data in the 50% range is above the median value.

The partition values that divide the data into four equal halves are called quartiles. The first quartile is the value below which 25% of the data is found and above which 75% of the data is found. The median is represented by the second quartile. The third quartile is the value below which 75% of the data is found, and beyond which 25% of the data is found.

In the given example, we are given the below parameters about the population:

$$\begin{gathered} \mu =1000\mathrm{FTES} \\ median=1014FTES \\ \sigma =474FTES \\ firstquartile=528.5\mathrm{FTES} \\ thirdquartile=1447.5FTES \\ n=29years \end{gathered}$$

We must determine the 75% of all years with an FTES at or below a certain value, as well as the 75% of all years with an FTES at or above a certain value.

We know that 75% of data falls below the third quartile figure, thus we have: 75% of all years with an FTES of 1447.5 or less.

We also know that 75% of data is above the first quartile value, so we have: 75% of all years with an FTES of 528.5 or above.