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 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: Calculate total blue - marbles in samples

Count blue - marbles in each sample. There is 1 sample with 3 blue marbles, 1 sample with 5 blue marbles, 4 samples with 6 blue marbles, 7 samples with 7 blue marbles, 6 samples with 8 blue marbles, and 1 sample with 9 blue marbles.
\[3\times1 + 5\times1+6\times4 + 7\times7+8\times6 + 9\times1=3 + 5+24 + 49+48 + 9=138\]

Step2: Calculate total marbles in all samples

Since each sample has 10 marbles and there are 20 samples, the total number of marbles in all samples is \(10\times20 = 200\).

Step3: Calculate percentage of blue marbles

The percentage of blue marbles is \(\frac{138}{200}\times100\%=69\%\). The closest option to 69% is 75%.

Answer:

A. 75%