A random sample of house sizes in major city has a sample mean of x¯=1204.9 sq ft and sample standard deviation of s=124.6 sq ft. Use the Empirical Rule to determine the approximate percentage of house sizes that lie between 955.7 and 1454.1 sq ft. Round your answer to the nearest whole number (percent).

Question

Mathematics

Ansley

18 December, 04:17

A random sample of house sizes in major city has a sample mean of x¯=1204.9 sq ft and sample standard deviation of s=124.6 sq ft. Use the Empirical Rule to determine the approximate percentage of house sizes that lie between 955.7 and 1454.1 sq ft. Round your answer to the nearest whole number (percent).

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Denise Graves · Answer 1

About 95% of house sizes that lie between 955.7 and 1454.1 sq ft.

Step-by-step explanation:

According to the empirical rule about 68% of the data is within one standard deviation of the mean; about 95% of the data is within two standard deviations of the mean; about 99.7% of the data is within three standard deviations of the mean.

We have given:

Sample mean : x¯=1204.9 sq ft

Standard deviation: s=124.6 sq ft

To find the percentage of house sizes that lie between 955.7 and 1454.1 sqft.

We can write it as

955.7 = 1204.9 - 249.2 = 1204.9 - 2 (124.6)

and 1454.1 = 1204.9 + 249.2 = 1204.9 + 2 (124.6)

Thus, 955.7 is 2 standard deviations left from the means and 1454.1 is 2 deviations right from the mean.

Then by empirical rule, about 95% of house sizes that lie between 955.7 and 1454.1 sq ft.