A group of people estimate the number of Blue m&m's in a large jar. They each take a sample of 20 m&m's and count the number of blue m&m's before returning them to the jar. Here is the data from the samples:Number of Blue m&m's Number of Samples4 25 56 97 78 39 110 211 1 If it is revealed that there are actually 1200 m&m's in the jar, then what is the best estimate of the number of blue m&m's?

To estimate the number of blue M&M's in the jar, we first need to calculate the average number of blue M&M's from the samples taken.

Here's how to do it:

1. Multiply the number of blue M&M's by the number of samples for each row, then sum up these results. This gives us the total number of blue M&M's from all samples.

   (42) + (55) + (69) + (77) + (83) + (91) + (102) + (111) = 8 + 25 + 54 + 49 + 24 + 9 + 20 + 11 = 200

2. Sum up the number of samples to get the total number of samples.

   2 + 5 + 9 + 7 + 3 + 1 + 2 + 1 = 30

3. Divide the total number of blue M&M's from all samples by the total number of samples to get the average number of blue M&M's per sample.

   200 / 30 = 6.67

This means that on average, there are about 6.67 blue M&M's in a sample of 20 M&M's.

4. To estimate the total number of blue M&M's in the jar, we need to scale up this average to the total number of M&M's in the jar. Since there are 1200 M&M's in the jar and each sample is 20 M&M's, there are 1200 / 20 = 60 samples in the jar.

5. Multiply the average number of blue M&M's per sample by the total number of samples in the jar.

   6.67 * 60 = 400.2

So, the best estimate of the number of blue M&M's in the jar is approximately 400.

To estimate the number of blue M&M's in the jar, we first need to calculate the average number of blue M&M's per sample. We do this by multiplying the number of blue M&M's by the number of samples for each row, summing these products, and then dividing by the total number of samples.

Here's the calculation:

(42) + (55) + (69) + (77) + (83) + (91) + (102) + (111) = 8 + 25 + 54 + 49 + 24 + 9 + 20 + 11 = 200

The total number of samples is 2 + 5 + 9 + 7 + 3 + 1 + 2 + 1 = 30

So, the average number of blue M&M's per sample is 200 / 30 = 6.67

Since each sample contains 20 M&M's, we can estimate that about 6.67 / 20 = 0.3335 of the M&M's in the jar are blue.

Finally, we multiply this proportion by the total number of M&M's in the jar to estimate the total number of blue M&M's:

0.3335 * 1200 = 400

So, the best estimate of the number of blue M&M's in the jar is 400.