Questions: A frequency distribution is shown below. Complete parts (a) and (b). The number of televisions per household in a small town Televisions: 0, 1, 2, 3 Households: 24, 445, 728, 1405 (a) Use the frequency distribution to construct a probability distribution. x P(x) 0 1 2 3 (Round to three decimal places as needed.) (b) Graph the probability distribution using a histogram. Choose the correct graph of the distribution below. A. B. C. Describe the histogram's shape. Choose the correct answer below. - skewed left - symmetric

Solution Steps

Sum the number of households for each category of televisions: \[ 24 + 445 + 728 + 1405 = 2602 \]

Calculate the probability \( P(x) \) for each number of televisions \( x \) by dividing the number of households by the total number of households (2602). Round to three decimal places.

\[ P(0) = \frac{24}{2602} \approx 0.009 \] \[ P(1) = \frac{445}{2602} \approx 0.171 \] \[ P(2) = \frac{728}{2602} \approx 0.280 \] \[ P(3) = \frac{1405}{2602} \approx 0.540 \]

Compare the calculated probabilities with the histograms provided. The correct histogram should reflect the probabilities:

• \( P(0) \approx 0.009 \)
• \( P(1) \approx 0.171 \)
• \( P(2) \approx 0.280 \)
• \( P(3) \approx 0.540 \)

The correct histogram is C.

Final Answer