Questions: Pizza Sales Construct a probability distribution for the data and draw a graph for the distribution. The probability that a pizza shop sells 3, 8 , or 11 pizzas to one person is 1/25, 21/25, or 3/25 respectively.

Solution Steps

We are given the following probabilities:

• P(X=3) = 1/25
• P(X=8) = 21/25
• P(X=11) = 3/25

We can represent this information in a table:

| X | P(X) | |---|---| | 3 | 1/25 | | 8 | 21/25 | | 11 | 3/25 |

A probability distribution must satisfy two conditions:

1. Each probability must be between 0 and 1 (inclusive).
2. The sum of all probabilities must equal 1.

In our case, all probabilities are between 0 and 1. Let's check the sum:

(1/25) + (21/25) + (3/25) = (1+21+3)/25 = 25/25 = 1

Since both conditions are met, this is a valid probability distribution.

We can represent the distribution graphically using a histogram or a bar chart. The x-axis represents the number of pizzas sold (X), and the y-axis represents the probability P(X).

• For X = 3, the probability is 1/25 = 0.04.
• For X = 8, the probability is 21/25 = 0.84.
• For X = 11, the probability is 3/25 = 0.12.

The graph would have three bars:

• A bar at X = 3 with a height of 0.04.
• A bar at X = 8 with a height of 0.84.
• A bar at X = 11 with a height of 0.12.

Final Answer