To determine how many of the next 1500 pizzas Valentino's Pizzeria should expect to be thick crust or thin crust, follow these steps:
1. Determine the total number of pizzas sold last week:
- Thin crust: 307
- Thick crust: 225
- Stuffed crust: 161
- Pan style: 180
Total number of pizzas sold last week:
[tex]\[
307 + 225 + 161 + 180 = 873
\][/tex]
2. Calculate the probabilities of each type of crust being sold:
- Probability of a thin crust pizza:
[tex]\[
\frac{307}{873} \approx 0.3518
\][/tex]
- Probability of a thick crust pizza:
[tex]\[
\frac{225}{873} \approx 0.2576
\][/tex]
3. Calculate the expected number of each type of pizza in the next 1500 pizzas:
- Expected number of thin crust pizzas:
[tex]\[
0.3518 \times 1500 \approx 527.49
\][/tex]
- Expected number of thick crust pizzas:
[tex]\[
0.2576 \times 1500 \approx 386.60
\][/tex]
4. Calculate the total expected number of thin and thick crust pizzas:
[tex]\[
527.49 + 386.60 \approx 914.09
\][/tex]
5. Round to the nearest whole number:
- Expected number of thin crust pizzas:
[tex]\[
\approx 527
\][/tex]
- Expected number of thick crust pizzas:
[tex]\[
\approx 387
\][/tex]
- Total expected number of thin and thick crust pizzas:
[tex]\[
\approx 914
\][/tex]
Therefore, Valentino's Pizzeria should expect approximately 527 thin crust pizzas and 387 thick crust pizzas, totaling 914 pizzas, of the next 1500 pizzas sold to be either thick crust or thin crust.
