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Alonzo'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 a 
32% chance of getting a cupcake, a 
52% chance of getting a brownie, and a 
16% chance of getting a muffin.
Alonzo wants to simulate what could happen for the first ten customers.
So for each customer, he generates a random whole number from 1 to 100 .
(a) What is a range of values that Alonzo can use to represent a customer getting a brownie?

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(b) Here is Alonzo's simulation.




Customer
1
2
3
4
5
6
7
8
9
10


Random number
48
83
1
53
52
23
8
10
37
85




Using your answer in part (a), find the percentage of the 10 simulated customers who got a brownie.

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%

Alonzo'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 a 32% 32 \% chance of getting a cupcake, a 52% 52 \% chance of getting a brownie, and a 16% 16 \% chance of getting a muffin.\newlineAlonzo wants to simulate what could happen for the first ten customers.\newlineSo for each customer, he generates a random whole number from 11 to 100100 .\newline(a) What is a range of values that Alonzo can use to represent a customer getting a brownie?\newline \square to \square \newline(b) Here is Alonzo's simulation.\newline\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|}\newline\hline Customer & 11 & 22 & 33 & 44 & 55 & 66 & 77 & 88 & 99 & 1010 \\\newline\hline Random number & 4848 & 8383 & 11 & 5353 & 5252 & 2323 & 88 & 1010 & 3737 & 8585 \\\newline\hline\newline\end{tabular}\newlineUsing your answer in part (a), find the percentage of the 1010 simulated customers who got a brownie.\newline \square % \%

Full solution

Q. Alonzo'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 a 32% 32 \% chance of getting a cupcake, a 52% 52 \% chance of getting a brownie, and a 16% 16 \% chance of getting a muffin.\newlineAlonzo wants to simulate what could happen for the first ten customers.\newlineSo for each customer, he generates a random whole number from 11 to 100100 .\newline(a) What is a range of values that Alonzo can use to represent a customer getting a brownie?\newline \square to \square \newline(b) Here is Alonzo's simulation.\newline\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|}\newline\hline Customer & 11 & 22 & 33 & 44 & 55 & 66 & 77 & 88 & 99 & 1010 \\\newline\hline Random number & 4848 & 8383 & 11 & 5353 & 5252 & 2323 & 88 & 1010 & 3737 & 8585 \\\newline\hline\newline\end{tabular}\newlineUsing your answer in part (a), find the percentage of the 1010 simulated customers who got a brownie.\newline \square % \%
  1. Allocate Percentages: To find the range for brownies, we need to allocate the percentages to the numbers 11 to 100100. Since cupcakes have a 32%32\% chance, they would take the first 3232 numbers. Brownies come next with a 52%52\% chance.
  2. Calculate Brownies Range: The range for brownies starts after the last number for cupcakes. So, it starts at 3333 and goes up to 33+521=8433 + 52 - 1 = 84. The range for brownies is 3333 to 8484.
  3. Count Numbers in Range: Now, we count how many random numbers fall within the range for brownies. The numbers in the simulation are 4848, 8383, 11, 5353, 5252, 2323, 88, 1010, 3737, and 8585. Numbers 4848, 8383, 5353, and 5252 are in the range for brownies.
  4. Calculate Percentage: There are 44 numbers within the range for brownies out of 1010 customers. To find the percentage, we calculate (410)×100%=40%(\frac{4}{10}) \times 100\% = 40\%.

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