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 returned to the jar after each sample, and the marbles are remixed. the results of the first 20 samples are shown in the dot plot. number of blue marbles out of 10 0 1 2 3 4 5 6 7 8 9 10 based on the samples, which would be the best guess for the percentage of blue marbles in the jar? a 65% b 55% c 35% d 15%

Explanation:

Step1: Count total blue marbles in samples

Count dots in dot - plot. There are 2 dots at 1, 5 dots at 2, 7 dots at 3, 4 dots at 4, 1 dot at 5, 1 dot at 6, 0 dots at 7 - 10. Total blue marbles = \(2\times1 + 5\times2+7\times3 + 4\times4+1\times5+1\times6=2 + 10+21 + 16+5+6 = 60\).

Step2: Calculate average number of blue marbles per sample

There are 20 samples, and each sample has 10 marbles. Average number of blue marbles per sample=\(\frac{60}{20}=3\).

Step3: Calculate percentage of blue marbles

Percentage of blue marbles=\(\frac{3}{10}\times100\% = 30\%\), which is closest to 35% among the given options.

Answer:

C. 35%