Let's break down and solve each part of the problem step-by-step.
### Part (a)
Question:
What is a range of values that the game operator can use to represent a winner getting a stuffed animal?
Solution:
A winner has a 57% chance of getting a stuffed animal. To simulate this using random numbers from 1 to 100, we assign the first 57 numbers (1 to 57) to getting a stuffed animal.
Thus, the range of values representing a winner getting a stuffed animal is from:
[tex]\[1 \text{ to } 57\][/tex]
### Part (b)
Question:
Given the random numbers drawn by the winners, find the percentage of the 10 simulated winners who got a stuffed animal.
Solution:
To determine how many winners got a stuffed animal, we look at the random numbers and see if they fall within the range 1 to 57.
Here are the random numbers drawn by each winner:
[tex]\[41, 58, 4, 23, 72, 1, 5, 47, 44, 52\][/tex]
We count how many of these numbers are within the range 1 to 57:
- 41 is within 1 to 57
- 58 is not within 1 to 57
- 4 is within 1 to 57
- 23 is within 1 to 57
- 72 is not within 1 to 57
- 1 is within 1 to 57
- 5 is within 1 to 57
- 47 is within 1 to 57
- 44 is within 1 to 57
- 52 is within 1 to 57
Counting the qualifying numbers, we find there are 8 winners who got a stuffed animal.
To find the percentage of winners who got a stuffed animal:
[tex]\[
\text{Percentage} = \left( \frac{\text{Number of winners who got stuffed animals}}{\text{Total number of winners}} \right) \times 100
\][/tex]
[tex]\[
\text{Percentage} = \left( \frac{8}{10} \right) \times 100 = 80\%
\][/tex]
Thus, the percentage of the 10 simulated winners who got a stuffed animal is:
[tex]\[80\% \][/tex]
### Summary:
(a) Range of values representing a winner getting a stuffed animal:
[tex]\[1 \text{ to } 57\][/tex]
(b) Percentage of the 10 simulated winners who got a stuffed animal:
[tex]\[80\% \][/tex]
