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In this problem, we explare the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set. 13,7, 9,3, 10 AT XK (a) Use the defining formula, the computation formula, or a calculator to compute &, (Round your answer to four decimal places.) N See the rounding prompt for how many decimal places are needed. (b) Add S to each data value to get the new data set 18, 12, 14, 8, 24, Compute 5. (Round your answer to four decimal places.) time to failure (in hours) at 90% breaking strength. Kevlar epoxy is a material used on the NASA space shuttles. Strands of this epoxy were tested at the 90% breaking strength. The following data represent time to failure (in hours) for a random sample of 50 epoxy strands. Let x be a random variable representing 0.55 1.80 1.52 2.05 1.03 1.18 0.80 1.33 1.29 1.15 3.34 1.54 0.08 J. 12 0.60 0.72 0.9 1.05 1.43 3.04 1.81 2.1 0.63 0.56 0.03 1.09 J. 18 0.34 1.51 1.45 1.52 0. 1 1.55 0.01 0.07 0.65 3.40 0.24 1.51 1.45 1.60 1.80 4.69 D.08 7.89 1.58 1.65 0,03 0.23 0.72 LO USE SALT (a) Find the range. 7.88 (b) Use a calculator to calculate Ex and Ex2. EX = X Ex2 = x (c) Use the results of part (b) to compute the sample mean, variance, and standard deviation for the time to failure. (Round your answers to four decimal places. ) X = X X X (d) Use the results of part (c) to compute the coefficient of variation (in percent). (Round your answer to the nearest whole number.)What was the age distribution of prehistaric Native Americans? Suppose an extensive anthropological studies in the southwestern United States gave the fallowing information about a prehistoric extended family group of 87 members on what is now a Native American reservation Age range (years) 1-10 | 11-20 | 21-30 | 31 and over Number of individuals 31 19 25 12 For this community, estimate the mean age expressed in years, the sample variance, snd the sample standard deviation, For the class 31 and over, use 35.5 as the class midpoint. (Round your answers to one decimal place.) X = K years what percentage of the general U.S. population have bachelor's degrees? Suppose the percentage of bachelor's degrees by state are as follows. For convenience, the data are sorted in increasing order. 16 (17 (18 (10| 10| 19 | 20 | 20 | 20 | 21| 21 | 21 | 22 | 22 | 22 | 23 | 23 23 (23 (22 | 22| 23 | 23| 23 | 25 | 25 | 25| 25 | 25 | 25 | 25 | 28 | 26 | 26 26 (27 (27 |27 |27 |28 |28 |28 |28 | 30| 31 | 31|32 |33 | 34| 39 (3) Select the box-and-whisker plot i - (b) Find the interquartile rangs. IGR = (c) 4 particular state has a bachelor's degree percentage rate of about 26%. Into what guarter does this rate fall? below between Q, and the median between the median and Q, above y Consumer Reports rated automobile insurance companies and gave annual premiums for top-rated companies in several states. The figure below shows box plots for annual premiums for urban customers (married couple with one 17-year-old son) in the box plots were all drawn using the same scale on a TI-84Plus/TI-83Plus calculator. Texas Pennsylvania California (a) Which state has the lowest premium? O Texas O Pennsylvania O California Which state has the highest premium? O Texas O Pennsylvania O California (b) Which state has the highest median premium? O Texas O Pennsylvania O California (c) Which state has the smallest range of premiums? O Texas O Pennsylvania O California(c) Which state has the smallest range of premiums? O Texas O Pennsylvania O California Which state has the smallest interquartile range? O Texas O Pennsylvania O California (d) The five-number summaries generated on the TI-84Plus/TI-83Plus calculators for the box plots are given below. Five-Number Summaries for Insurance Premiums Summary (i): Summary (ii): Summary (iii): 1-Var Stats 1-var Stats 1-Var Stats In=10 In=10 In=10 minx=2382 minx=3314 minx=2323 Q1=2758 01=4326 Q1=2801 Med=2991 Med=5116.5 Med=3377. 5 23=3652 23=5801 23=3966 maxx=5715 maxX=7527 maxx=4482 Match the five-number summaries to the appropriate box plots. The five-number summary for Texas is summary ---Select--- v . The five-number summary for Pennsylvania is summary ---Select--- v . The five-number summary for California is summary ---Select--- v