number 39 Sale Price of Homes The average sale price of one-family houses in the

Question

number 39

Sale Price of Homes The average sale price of one-family houses in the United States for January 2016 was $258, 100. Find the range of values in which at least 75% of the sale prices will lie if the standard deviation is $48, 5000. Source: YCharts.com Trials to Learn Maza The average of the number of trials it took a sample of mice to leant to traverse a maze was 12. The standard deviation was 3. Using Chebyshev's theorem, find the minimum percentage of data values that will fall in the range of 4-20 trials. Farm Sizes The average farm in the United States in 2014 contained 504 acres. The standard deviation is 55.7 acres. Use Chebyshev's theorem to find the minimum percentage of data values that will fall in the range of 392.5 and 896.57 acres. Source: World Almanac. Citrus Fruit Consumption The average U.S. yearly per capita consumption of citrus fruit is 26.8 pounds. Suppose that the distribution of fruit amounts consumed is bell-shaped with a standard deviation equal to 4.2 pounds. What percentage of Americans would you expect to consume more than 31 pounds of citrus fruit per year? Sourer: USDA/Economic Research Service. SAT Scores The national average for mathematics SATs in 2014 was 538. Suppose that the distribution of scores was approximately bell-shaped and that the standard deviation was approximately 48. Within what boundaries.

Explanation / Answer

Question 39:

Here the mean size is given to be 504 acres with a standard deviation of 55.7 acres.

Now according to the chebyshev's inequality at least 11/k2 of the distribution's values are within k standard deviations of the mean.

Therefore here we have been given,

392.5 = which is roughly 2 standard deviations. Now according to the chebyshev's inequality at least 1 - 1/22 = 0.75 proportion of total values must lie within 2 standard deviations of the mean.

Therefore, at most 0.25 proportion of values must like outside it that is 0.25/2 = 0.125 on either side outside the 2 standard deviations group. proportion of values below 392.5 thus would be 0.125 here.

Now 896.57 = 392.5 + 9.05*55.7 that is it is above 9.05 standard deviations of the mean. By chebyshev's inequality at least 1 - (1/ 9.052) = 0.9878 of the values must lie within 9.05 standard deviations of the mean that is at most (1 - 0.9878) = 0.0122 must lie beyond outside 9.05 standard deviations that is 0.0122/2 = 0.0061 proportion of values at most lie outside on either side.

Therefore for the given interval, at most (0.0061 + 0.125 ) = 0.1311 proportion of the values must lie outside this interval. and therefore 1 - 0.1311 = 0.8689 therefore at least 86.89% of the values must lie within the given interval.

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.