ΣΧ. Σ ΣΧ Σ. .2 х, i=1 i=1 п or s = -. Find the mean and %3D formulas given by s? п -1 п-) п-1 standard deviation for the set n= {5,7,1,2,4}. 9 Find the mean, median, mode and standard deviation for the set - {40,56,38,38,63,59,52,49,46} and describe the sample in terms of the measures of %3D central tendency and variability.? 10. The number of classes for a histögram is determined by NC =1+3.33log1o n, the class width %3D L-S Construct a frequency histogram for a set of GPAS of thirty is determined by CW : %3D NC randomly selected students: 2,0, 3.1, 1,9,2.3, 1,9,2.3)2.6, 3.1,2.5, 2.1, 2.9, 3.0, 2.7, 2,5.2.4, 2.7, 2,5, 2.4, 3.0, 3.4, 2.6, 2.8, 2.3, 2.7, 2.9, 2.7, 2.8, 2.2) 2.7, 21 7 11. Suppose that the budget for supplies in a small business is, on the average, $450.00 per month with a variability of $50.00. Assuming that the expenditures are normally distributed, then determine the proportion or the probability that the budget would be exceeded by $50.00 in any given month. 12. Tchebysheff's Theorem: Given a number k greater than or equal to 1 and a set of n 1-( of the measurements will lie within k measurements x,, X2, X3 ,., X, , at least standard deviations from the mean. Mathematically, Tchebysheff's theorem states that if X is a random variable with mean u and variance o' then for k >0 P||X-H< ko 21 or k2 1 Describe the distribution of 25 measurements that have a k? P(μ- ko 1 - mean of 75 and a variance of 100. Assume that there is doubt concerning the normality of the data. 13/The daily production of electronic motors at a certain factory averaged 120 with a standard deviation of 10. What can be said about the fraction of days that will have production levels between 100 and 140? Find the shortest interval to contain at least 90% of the daily production levels. Case Study Suppose you currently own a house in Eastville, Oregon, and are planning on moving sometime in the next year. A friend has suggested that you sell your house on your own; perhaps a difficult decision. Real estate commissions can be quite hefty, but brokers bring a great deal of expertise to the process of selling a house, particularly the ability to set a reasonable asking price. Real estate professionals can quantify a variety of unobservable or immeasurable characteristics of a house such as a type of wallpaper in an upstairs bathroom and the overall desirability of the neighborhood.