Chapter 14, Problem 1E

As part of a sixth-grade class project the teacher brings to class a large jar containing 200 gumballs of two different colors: red and green. Andy is asked to draw a sample of his own choosing and estimate the number of red gumballs in the jar. Andy draws a sample of 25 gumballs, of which 8 are red and 17 are green. Use Andy’s sample to estimate the number of red gumballs in the jar.

To determine

To find:

The number of red gumballs in the jar.

Answer to Problem 1E

Solution:

The numbers of red gumballs in the jar are approximately 64.

Explanation of Solution

Given:

Total numbers of gumballs in a jar are 200. Andy draws a sample of 25 gumballs, of which 8 are red and 17 are green.

Formula used:

Single- Sample Estimation Method:

$\frac{k}{n}\approx \frac{N}{P}\mathrm{...}(1)$

Where, $P$ is the size of the general population, $N$ is the size of the subpopulation, $n$ is the size of the sample, and $k$ is the number individuals belong to the subpopulation.

Calculation:

From the given information, substitute 200 for $P$, 25 for sample size $n$, 8 for $k$ in the equation $\left(1\right)$ as,

$\begin{array}{rll}\frac{k}{n}& \approx & \frac{N}{P}\\ \frac{8}{25}& \approx & \frac{N}{200}\\ N& \approx & \frac{8\times 200}{25}\end{array}$

Further simplify.

$\begin{array}{rll}N& =& \frac{1600}{25}\\ & =& 64\end{array}$

Conclusion:

Thus, the numbers of red gumballs in the jar are approximately 64.