Question

suppose that prices of a certain model of new homes are normally distributed with a mean of $150000. Use the 68-95-99.7 rule to find the percentage of buyers who paid: between $150000 and $154800 if the standard deviation is $1600

Answer 1

Using the Empirical Rule, it is found that 49.85% of buyers paid between $150,000 and $154,800.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

• Approximately 68% of the measures are within 1 standard deviation of the mean.

• Approximately 95% of the measures are within 2 standard deviations of  the mean.

• Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Considering the given mean and standard deviation, the interval between $150,000 and $154,800 corresponds to the interval between the mean and 3 standard deviations above the mean.

The normal distribution is symmetric(50% above the mean, 50% below), hence the percentage corresponding to this interval is:

P = 0.5 x 99.7% = 49.85%.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

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