Let's solve the problem step by step:
### Part (a)
First, we need to determine the ranges of values that represent each prize based on the given percentages:
- A 25% chance of getting a stuffed animal means numbers from 1 to 25.
- A 26% chance of getting a hat means numbers from 26 to 51.
- A 49% chance of getting a basketball means numbers from 52 to 100.
To answer part (a):
The range of values for getting a basketball is from 52 to 100.
### Part (b)
Next, we use the given random numbers to determine the percentage of winners who got a basketball. The table provides the following random numbers drawn by the winners:
Random numbers: 30, 86, 59, 24, 68, 74, 15, 50, 32, 66
We need to identify which of these numbers fall within the basketball range (52 to 100):
- Random number 30: Not within the range (stuffed animal)
- Random number 86: Within the range (basketball)
- Random number 59: Within the range (basketball)
- Random number 24: Not within the range (stuffed animal)
- Random number 68: Within the range (basketball)
- Random number 74: Within the range (basketball)
- Random number 15: Not within the range (stuffed animal)
- Random number 50: Not within the range (hat)
- Random number 32: Not within the range (hat)
- Random number 66: Within the range (basketball)
Counting the numbers that fall within the basketball range, we find there are 5 numbers (86, 59, 68, 74, 66).
Now, to calculate the percentage of winners who got a basketball, we use the following formula:
[tex]\[ \text{{Percentage}} = \left( \frac{{\text{{Number of basketball winners}}}}{{\text{{Total number of winners}}}} \right) \times 100 \][/tex]
Plugging in the values:
[tex]\[ \text{{Percentage}} = \left( \frac{5}{10} \right) \times 100 = 50\% \][/tex]
To answer part (b):
The percentage of the 10 simulated winners who got a basketball is [tex]$50\%$[/tex].
