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Lamar's Bakery is giving a treat to each customer at a grand opening event. Each customer spins a wheel to determine which treat they get. Every customer has an [tex]$18\%$[/tex] chance of getting a tart, a [tex]$31\%$[/tex] chance of getting a pie, and a [tex]$51\%$[/tex] chance of getting a snickerdoodle.

Lamar wants to simulate what could happen for the first ten customers. For each customer, he generates a random whole number from 1 to 100.

(a) What is a range of values that Lamar can use to represent a customer getting a snickerdoodle?
[tex]\[
\boxed{}
\boxed{}
\][/tex]

(b) Here is Lamar's simulation.
[tex]\[
\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|}
\hline
Customer & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
Random \, number & 54 & 73 & 51 & 9 & 18 & 30 & 48 & 56 & 36 & 76 \\
\hline
\end{array}
\][/tex]

Using your answer in part (a), find the percentage of the 10 simulated customers who got a snickerdoodle.
[tex]\[
\boxed{} \%
\][/tex]

Sagot :

GinnyAnsweridn
Certainly! Let's address the given problem step by step.

(a) What is a range of values that Lamar can use to represent a customer getting a snickerdoodle?

Given:
- The probability of getting a snickerdoodle is [tex]\(51\%\)[/tex].

Since Lamar generates a random whole number from 1 to 100 for each customer:
- The range of values that represents a [tex]\(51\%\)[/tex] chance will cover 51 values out of the 100 possible values.
- These values start immediately after the values representing the previous groups (tart and pie).

The probability ranges for each treat are:
- Tart: [tex]\(18\%\)[/tex], which can be represented by the numbers from 1 to 18.
- Pie: [tex]\(31\%\)[/tex], following the tart range, so represented by the numbers from 19 to 49.

Thus, the range for a snickerdoodle will begin right after the pie range:
- Snickerdoodle: From 50 to 100.

So the range of values that Lamar can use to represent a customer getting a snickerdoodle is:
[tex]\[50\][/tex] [tex]\(\square\)[/tex] to [tex]\[100\][/tex] [tex]\(\square\)[/tex]

(b) Here is Lamar's simulation:

Customer | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Random number | 54 | 73 | 51 | 9 | 18 | 30 | 48 | 56 | 36 | 76

Using the range [tex]\(50\)[/tex] to [tex]\(100\)[/tex] for a customer getting a snickerdoodle, let's identify which random numbers fall in this range:
- Customer 1: 54 (snickerdoodle)
- Customer 2: 73 (snickerdoodle)
- Customer 3: 51 (snickerdoodle)
- Customer 4: 9 (not a snickerdoodle)
- Customer 5: 18 (not a snickerdoodle)
- Customer 6: 30 (not a snickerdoodle)
- Customer 7: 48 (not a snickerdoodle)
- Customer 8: 56 (snickerdoodle)
- Customer 9: 36 (not a snickerdoodle)
- Customer 10: 76 (snickerdoodle)

Count the number of customers who got a snickerdoodle:
- There are 5 customers who got a snickerdoodle: Customer 1, 2, 3, 8, and 10.

To find the percentage of the 10 simulated customers who got a snickerdoodle:
[tex]\[ \text{Percentage} = \left( \frac{\text{Number of customers with a snickerdoodle}}{\text{Total number of customers}} \right) \times 100 \][/tex]

[tex]\[ \text{Percentage} = \left( \frac{5}{10} \right) \times 100 = 50.0\% \][/tex]

Hence, the percentage of the 10 simulated customers who got a snickerdoodle is:
[tex]\[ 50.0 \% \][/tex]
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