25 POINTS I WILL GIVE BRAINLIEST Patty’s Parasols recorded the monthly rainfall and their umbrella sales for an entire year. The following table shows the inches of rainfall and the number of umbrellas the store sold each month. The relationship between the inches of rainfall and umbrella sales can be modeled using a linear function. Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec. Rainfall (in.) 2.5 3.1 4.0 4.3 3.6 2.4 1.2 0.6 1.5 1.4 1.1 2.6 Umbrella sales 132 140 162 170 156 103 98 87 84 78 110 125 (a) Using technology, determine the correlation coefficient for the data to the nearest hundredth. Explain the steps you used. (b) What does the correlation coefficient for the data indicate about the direction and strength of the linear association between the monthly rainfall and the number of umbrellas sold?

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above