Question

eliza volunteers at a library. one day, she counts the number of books the first 20 people borrow. the list shows her data. 1,1,2,2,2,2,3,3,3,4,5,5,5,6,6,7,7,9,10,12 eliza uses the data points to make the probability distribution shown in the table below. use the drop - down menus to explain if the probability distribution represents the data. books borrowed from library | number of books | probability | | --- | --- | | 1 - 3 | 0.45 | | 4 - 6 | 0.3 | | 7 - 9 | 0.15 | | 10 - 12 | 0.1 | click the arrows to choose an answer from each menu. the probabilities in the table should be equal to the total number of choose... in each grouping divided by choose... the probability distribution choose... represent the data in the list.

Explanation:

Step1: Count data in each group

• 1 - 3: Numbers are 1,1,2,2,2,2,3,3,3. Count: 9.
• 4 - 6: Numbers are 4,5,5,5,6,6. Count: 6.
• 7 - 9: Numbers are 7,7,9. Count: 3.
• 10 - 12: Numbers are 10,12. Count: 2.

Total data points: \(9 + 6 + 3 + 2 = 20\), which matches the first 20 people.

Step2: Calculate probabilities

• Probability for 1 - 3: \(\frac{9}{20} = 0.45\) (matches table).
• Probability for 4 - 6: \(\frac{6}{20} = 0.3\) (matches table).
• Probability for 7 - 9: \(\frac{3}{20} = 0.15\) (matches table).
• Probability for 10 - 12: \(\frac{2}{20} = 0.1\) (matches table).

Step3: Check if distribution represents data

Since each calculated probability (from data count / total) matches the table's probabilities, the distribution represents the data.

Answer:

The probabilities in the table should be equal to the total number of data points in each grouping divided by 20 (the total number of data points). The probability distribution does represent the data in the list.