Question

at a school carnival, a large jar has been filled with marbles. all the marbles are either red or blue. the school is offering a prize for correctly guessing the percentage of blue marbles in the jar. students are allowed to pick a sample of 10 marbles to help them guess. the sample marbles are remixed. the marbles are returned to the jar after each sample, and the results of the first 20 samples are shown in the dot - plot. based on the samples, which would be the best guess for the percentage of blue marbles in the jar? a 75% b 60% c 50% d 85%

Explanation:

Step1: Count total number of samples

There are 20 samples (dots in the dot - plot).

Step2: Calculate sum of blue marbles in samples

\[3\times1 + 5\times1+6\times5 + 7\times7+8\times6+9\times2\]
\[=3 + 5+30 + 49+48+18\]
\[=153\]

Step3: Calculate average number of blue marbles per sample

The average number of blue marbles per sample is \(\frac{153}{20}=7.65\).

Step4: Calculate percentage of blue marbles

Since each sample has 10 marbles, the percentage of blue marbles is \(\frac{7.65}{10}\times100 = 76.5\%\approx75\%\)

Answer:

A. 75%