Question

A random sample of house sizes in major city has a sample mean of 1204.9 square feet and a sample standard deviation of 124.6 square feet. Use the Empirical rule to determine the approximate percentage of house sizes that lie between 955.7 and 1454.1 square feet. Round your answer to the nearest whole number (percent).

Answer 1

95% of house sizes lie between 955.7 and 1454.1 square feet.

Explanation:

The empirical rule formula states that:

68% of data falls within 1 standard deviations from the mean - between μ – σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

In the above question,

Mean (μ)= 1204.9 square feet

Standard deviation (σ) = 124.6 square feet.

We are to determine the approximate percentage of house sizes that lie between 955.7 and 1454.1 square feet.

Step 1

We have to find the number of standard deviation from the mean

μ – xσ

1204.9 - 124.6x = 955.7

1204.9 - 955.7 = 124.6x

249.2 = 124.6x

x = 249.2/124.6

x = 2

μ + xσ

1204.9 + 124.6x = 1454.1

124.6x = 1454.1 - 1204.9

124.6x = 249.2

x = 249.2/124.6

x = 2

Therefore from the calculation above, it is 2 standard deviations from the mean, hence: from the empirical formula above,

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ