Question

A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 41 years old, with a standard deviation of 12 years. Suppose that these measures are valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers.(a) According to Chebyshev's theorem, at least ( choose one 36%/56%/ 75%/84%/89% ) of the home buyers' ages lie between 17 years and 65 years.(b) According to Chebyshev's theorem, at least ( choose one 36%/56%/ 75%/84%/89% ) of the home buyers' ages lie between years 23 and 59 years.

Answer 1

Anse

Step-by-step explanation:

Part (a)

The range of age is between 17 and 65 years. These values are at two 2 standards deviation of the mean because

41 + 2(12) = 65

41 - 2(12) = 17

Where 41 is the mean and 12 is the standard deviation.

According to Chebyshev's theorem, at least 1 - 1/k² are at k standard deviations of the mean. Replacing k = 2, we get:

1 - 1/2² = 1 - 1/4 = 0.75 = 75%

Therefore, at least 75% of the home buyers' ages lie between 17 years and 65 years,

Part (b)

In the same way, 23 and 59 years are at 1.5 standard deviations of the mean because

41 + 1.5(12) = 59

41 - 1.5(12) = 23

Then, replacing k = 1.5, we get

1 - 1/(1.5)² = 1 - 1/2.25 = 0.56 = 56%

So, at least 56% of the home buyers' ages lie between 23 and 59 years.