Questions: The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is 2000 and the standard deviation is 135. What is the approximate percentage of buyers who paid between 2000 and 2270? %

Solution Steps

The mean price paid for the HD television is $2000, and the standard deviation is $135.

We need to find the percentage of buyers who paid between $2000 and $2270.

Calculate the Z-scores for $2000 and $2270 using the formula: \[ Z = \frac{X - \mu}{\sigma} \] For $2000: \[ Z_{2000} = \frac{2000 - 2000}{135} = 0 \] For $2270: \[ Z_{2270} = \frac{2270 - 2000}{135} \approx 2 \]

Using the Z-table, find the percentage of data below each Z-score.

• For \( Z = 0 \), the percentage is 50%.
• For \( Z = 2 \), the percentage is approximately 97.72%.

Subtract the percentage at \( Z = 0 \) from the percentage at \( Z = 2 \): \[ 97.72\% - 50\% = 47.72\% \]

Final Answer