Question

which the statements are valid inferences that can be made based on the table?
a on average, about \\(\frac{1}{4}\\) of customers prefer pineapple.
b on average, about 20% of customers prefer extra cheese.
c on average, about 30% of customers prefer pepperoni.
d on average, about \\(\frac{1}{3}\\) of customers prefer mushrooms.
e on average, about 50% of customers prefer pepperoni or pineapple.

	extra cheese	mushrooms	pepperoni	pineapple

Explanation:

Step1: Calculate total customers

First, we find the total number of customers by adding the number of customers for each topping. The number of customers for extra cheese is 12, mushrooms is 20, pepperoni is 15, and pineapple is 5. So total customers $= 12 + 20 + 15 + 5 = 52$.

Step2: Analyze each option

• Option A: Number of customers who prefer pineapple is 5. The fraction is $\frac{5}{52}\approx 0.096$ (about 10%), not $\frac{1}{4}$ (25%). So A is invalid.
• Option B: Number of customers who prefer extra cheese is 12. The percentage is $\frac{12}{52}\approx 0.23$ (about 23%), close to 20%. So B is a valid inference.
• Option C: Number of customers who prefer pepperoni is 15. The percentage is $\frac{15}{52}\approx 0.29$ (about 29%), not 30% exactly but close? Wait, 30% of 52 is $0.3\times52 = 15.6$. 15 is close but let's check other options. Wait, maybe I miscalculated total. Wait, maybe the table is: extra cheese:12, mushrooms:20, pepperoni:15, pineapple:5. Total is 12 + 20 + 15 + 5 = 52. For pepperoni, $\frac{15}{52}\approx 28.8\%$, not 30%. For option D: mushrooms is 20, $\frac{20}{52}\approx 0.38$ (38%), not $\frac{1}{3}$ (33.3%). For option E: pepperoni (15) + pineapple (5) = 20. $\frac{20}{52}\approx 0.38$, not 50%. So the most valid is B.

Answer:

B. On average, about 20% of customers prefer extra cheese.