Question

The experiment is to randomly select a human and measure his or her length. Identify the type of the sample space.

• A. Finite sample space
• B. Continuous sample space
• C. Infinite discrete sample space
• D. None of these

Answer 1

The correct option is B Continuous sample space

The experiment is to randomly select a human and measure his or her length.

Depending of how far reaching our means of selection is it is possible to consider a sample space of about $6.6$ billion humans inhabiting the planet Earth.

In this case, the height of the selected person becomes a random variable.

However, it is also possible to consider the sample space consisting of all possible values of height measurements of the world population.

The tallest man ever measured lived in the United States and had a height of $272$ cm $\left(8^{\prime }{11}^{\prime \prime }\right)$. The height of the shortest person is more difficult to determine. Zero is clearly the low bound, but, for a living adult, it may be safely raised to, say, $40$ cm.

This suggests a sample space which is a line segment $[40,272]$ in centimeters.

While at all times the human population is discrete, we may assume that in some height range near the normal average, all possible heights are realized making a continuous classification.

We know that, "A continuous sample space is one which takes values in one or more intervals."

Thus the sample space is a continuous sample space.