Questions: The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is 1200 and the standard deviation is 125. Use the Empirical rule for this question. Do not use the calculator or tables. What is the approximate percentage of buyers who paid more than 1575 ?

Solution Steps

The z-score measures how many standard deviations a value is from the mean. The formula is: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. In this case: z = (1575 - 1200) / 125 z = 3 $1575 is 3 standard deviations above the mean.

The Empirical Rule states that approximately 99.7% of the data falls within 3 standard deviations of the mean. This means the area outside of 3 standard deviations (both above and below) contains about 100% - 99.7% = 0.3% of the data.

Since the normal distribution is symmetrical, half of the 0.3% outside 3 standard deviations will be above 3 standard deviations and half below. Therefore, the percentage of buyers who paid more than $1575 is approximately 0.3% / 2 = 0.15%.

Final Answer