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The prices paid for a particular model of a new car are normally distributed with a mean of ksh 3500000 0 and standard deviation of ksh 150000 Use the 68-95-99.7 Empirical rule to find the percentage of buyers who paid 1. Ksh 3050000 and 3650000 2. Ksh 3200000 and 3350000

User DRD
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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%.

User Feng Chen
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