Answer:
Explanation:
To use the 68-95-99.7 Empirical rule, we need to convert the given prices to standard deviations from the mean using the formula:
z = (x - mu) / sigma
where:
x = the given price
mu = the mean price
sigma = the standard deviation
Once we have calculated the z-scores, we can use the Empirical rule to find the percentage of buyers who paid within a certain range of prices.
For the range of Ksh 3050000 and 3650000:
First, we need to calculate the z-scores for these two prices:
z1 = (3050000 - 3500000) / 150000 = -0.3
z2 = (3650000 - 3500000) / 150000 = 1.0
According to the Empirical rule, about 68% of the buyers paid within one standard deviation of the mean, about 95% paid within two standard deviations, and about 99.7% paid within three standard deviations.
Since z1 is -0.3 and z2 is 1.0, both of these z-scores fall within one standard deviation of the mean. Therefore, we can estimate that about 68% of buyers paid between Ksh 3050000 and 3650000 for this car model.
For the range of Ksh 3200000 and 3350000:
Again, we need to calculate the z-scores for these two prices:
z1 = (3200000 - 3500000) / 150000 = -0.2
z2 = (3350000 - 3500000) / 150000 = -1.0
Both of these z-scores fall within one standard deviation of the mean, so we can again estimate that about 68% of buyers paid between Ksh 3200000 and 3350000 for this car model.
Therefore, the percentage of buyers who paid between Ksh 3050000 and 3650000 is about 68%, and the percentage of buyers who paid between Ksh 3200000 and 3350000 is also about 68%.