standard_description: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.
problem_activity: A city planner for a neighborhood of Boston is trying to determine if a new park should be built in the neighborhood. She goes around the neighborhood, knocking on doors, asking, “How many children under the age of 7 live in this household?” The data she collected from 28 households is shown in the frequency table below.
| **           # of children under 7 years old in the household          ** | **           Frequency          ** |
|---------------------------------------------------------------------------|------------------------------------|
|                                     0                                     |                 9                  |
|                                     1                                     |                 6                  |
|                                     2                                     |                 8                  |
|                                     3                                     |                 4                  |
|                                     4                                     |                 0                  |
|                                     5                                     |                 1                  |
a.   Create a dot plot to represent the data. Describe your dot plot in words.
b.   What number would you use to represent the center of the data? Explain why you chose that number.
c.   Based on the data, what would you recommend to the city planner about the new park? Does this neighborhood seem like a good place to put the new park? Explain why or why not using the data.


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