Questions: The table shows the distribution of family size in a certain U.S. city. t family is selected at random from the city. Find the probability that the size of the family is between 2 and 5 inclusive. Round approximations to three decimal places. Family Size Probability 2 0.442 3 0.236 4 0.195 5 0.071 6 0.037 7+ 0.019 A. 0.873 B. 0.431 C. 0.513 D. 0.944

The table shows the distribution of family size in a certain U.S. city. t family is selected at random from the city. Find the probability that the size of the family is between 2 and 5 inclusive. Round approximations to three decimal places. Family Size Probability 2 0.442 3 0.236 4 0.195 5 0.071 6 0.037 7+ 0.019 A. 0.873 B. 0.431 C. 0.513 D. 0.944
Transcript text: The table shows the distribution of family size in a certain U.S. city. $t$ family is selected at random from the city. Find the probability that the size of the family is between 2 and 5 inclusive. Round approximations to three decimal places. \begin{tabular}{|c|c|} \hline Family Size & Probability \\ \hline 2 & 0.442 \\ \hline 3 & 0.236 \\ \hline 4 & 0.195 \\ \hline 5 & 0.071 \\ \hline 6 & 0.037 \\ \hline $7+$ & 0.019 \\ \hline \end{tabular} A. 0.873 B. 0.431 C. 0.513 D. 0.944
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Solution

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Solution Steps

Step 1: Identify the relevant probabilities

The question asks for the probability that the family size is between 2 and 5 inclusive. From the table, the relevant probabilities are:

  • Family size 2: \( P(2) = 0.442 \)
  • Family size 3: \( P(3) = 0.236 \)
  • Family size 4: \( P(4) = 0.195 \)
  • Family size 5: \( P(5) = 0.071 \)
Step 2: Sum the probabilities

To find the probability that the family size is between 2 and 5 inclusive, we sum the probabilities for family sizes 2, 3, 4, and 5: \[ P(2 \leq \text{Family Size} \leq 5) = P(2) + P(3) + P(4) + P(5) \] \[ P(2 \leq \text{Family Size} \leq 5) = 0.442 + 0.236 + 0.195 + 0.071 \] \[ P(2 \leq \text{Family Size} \leq 5) = 0.944 \]

Step 3: Round the result

The result \( 0.944 \) is already rounded to three decimal places.

Final Answer

The probability that the family size is between 2 and 5 inclusive is \(\boxed{0.944}\). The correct choice is D.

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