Math  /  Data & Statistics

QuestionPart 2 of 2
A bowl contains blue and pink marbles. A scoop of marbles that is a representative sample contains 39 blue marbles and 26 pink marbles. a. Can you predict if there are more blue marbles or more pink marbles in the bowl? Explain. b. There are 750 marbles in a bowl. If you pick one marble from the bowl, are you more likely to pick a blue marble or a pink marble? a. Can you predict if there are more blue marbles or more pink marbles in the bowl? Explain. Choose the correct answer below. Yes. Because the representative sample contains more blue marbles than pink marbles, you can predict that the bowl contains more blue marbles than pink marbles. B. No. Because the sample is random, there is no way to predict what the bowl contains. C. No, because it is unknown whether the bowl contains other colored marbles D. Yes. Because the representative sample contains more pink marbles than blue marbles, you can predict that the bowl contains more pink marbles than blue marbles. b. There are 750 marbles in a bowl. If you pick one marble from the bowl, are you more likely to pick a blue marble or a pink marble?
If there are 750 marbles in the bow, then there are about \square blue marbles and \square pink marbles. So, you are \square marble.

Studdy Solution

STEP 1

What is this asking? Given a representative sample of marbles with 3939 blue and 2626 pink, can we guess if there are more blue or pink marbles in the bowl, and if the bowl has 750750 marbles, how many of each color are there? Watch out! A representative sample tells us about the *proportions* in the larger group, not the exact numbers!

STEP 2

1. Predict the majority color.
2. Calculate the total marbles in the sample.
3. Find the proportion of blue marbles.
4. Find the proportion of pink marbles.
5. Calculate the number of blue marbles in the bowl.
6. Calculate the number of pink marbles in the bowl.
7. Determine which color is more likely to be picked.

STEP 3

Since the sample has more blue (3939) than pink (2626) marbles, and it's a *representative* sample, we can **predict** there are more blue marbles in the bowl!

STEP 4

To find the total marbles in the sample, we **add** the number of blue marbles and the number of pink marbles: 39+26=6539 + 26 = 65.
So, our sample has a **total** of 6565 marbles.

STEP 5

The proportion of blue marbles is the number of blue marbles **divided** by the total number of marbles in the sample: 3965\frac{39}{65}.
We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 13.
So, 3965=39÷1365÷13=35\frac{39}{65} = \frac{39 \div 13}{65 \div 13} = \frac{3}{5}.
This means 35\frac{3}{5} of the marbles in the sample are blue!

STEP 6

Similarly, the proportion of pink marbles is the number of pink marbles **divided** by the total number of marbles: 2665\frac{26}{65}.
Simplifying this fraction gives us 2665=26÷1365÷13=25\frac{26}{65} = \frac{26 \div 13}{65 \div 13} = \frac{2}{5}.
So, 25\frac{2}{5} of the marbles in the sample are pink!
Notice that 35+25=55=1\frac{3}{5} + \frac{2}{5} = \frac{5}{5} = 1, which makes sense since all marbles are either blue or pink!

STEP 7

If the bowl has 750750 marbles, and we expect the same proportion of blue marbles as in the sample, we **multiply** the total number of marbles in the bowl by the proportion of blue marbles: 75035=75035=22505=450750 \cdot \frac{3}{5} = \frac{750 \cdot 3}{5} = \frac{2250}{5} = 450.
So, we predict there are 450450 blue marbles in the bowl!

STEP 8

We do the same for pink marbles: 75025=75025=15005=300750 \cdot \frac{2}{5} = \frac{750 \cdot 2}{5} = \frac{1500}{5} = 300.
We predict there are 300300 pink marbles in the bowl!
Notice that 450+300=750450 + 300 = 750, which is the total number of marbles in the bowl!

STEP 9

Since there are more blue marbles (450450) than pink marbles (300300), you are more likely to pick a blue marble!

STEP 10

a. Yes. Because the representative sample contains more blue marbles than pink marbles, you can predict that the bowl contains more blue marbles than pink marbles. b. If there are 750750 marbles in the bowl, then there are about 450450 blue marbles and 300300 pink marbles.
So, you are more likely to pick a blue marble.

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