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The following data represents the age of 30 lottery winners. 21 26 27 30 32 33 Complete the frequency distribution for the data. Bin Frequency [20,30) [30,40) [40,50) [50,60) [60,70) [70,80) [80,90) Here is 34 39 42 40 24 40 39 47 39 43 r discrete data 46 39 42 35 53 31 45 34 43 40 64 40 46 50 30 51 36 42 40 22 40 30 51 44 51 62 45 28 46 46 79 34 48 42 32 45 25 23 39 39 49 46 31 37 36 37 49 43 39 44 42 34 53 47 48 43 42 43 44 53 32 25 57 42 50 43 44 48 43 46 First, sort the data. Second, build a GFDT for this table with a classwidth of 5. (Be sure your lower class limits are multiples of the classwidth.) Next, answer the following questions about the data set: 1. What is the first lower class limit in your GFDT (given the classwidth of 5)? 2. Express the fourth class as a closed interval, i.e., [a' b] 3. Give the frequency for the fourth class. 4. What is the (arithmetic) mean for this data (report accurate to one decimal place)? 5. Usin the GFDT, what is the mode for this data set (use the appropriate definition for mode)? 6. What is the standard deviation for this data (report accurate to two decimal places)? 7. What is the five number summary for this data set (separate numbers with a comma)? 8. What is the IQR? 9. What usual score (i.e., non-outlier) has the largest positive zscore less than z = 2? (Give the data value, not the zscore.) 10. Give the would suggest something other than the mild outliers at the maximal end of the data set; report as a closed interval, i.e., [upper mild fence, upper extreme fence]. company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 207.2-cm and a standard deviation of 2.4-cm. Find the probability that the length of a randomly selected steel rod is between 209.1 -cm and 214.6-cm. P(209.1-cm < X < 214.6-cm) = Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z- scores rounded to 3 decimal places are accepted. A study was conducted to determine whether there were significant differences between college students admitted through special programs (such as retention incentive and guaranteed placement programs) and college students admitted through the regular admissions criteria. It was found that the graduation rate was 90.1% for the college students admitted through special programs. If 9 of the students from the special programs are randomly selected, find the probability that at least 8 of them graduated. prob = If 9 of the students from the special programs are randomly selected, find the probability that eactly 6 of them graduated. prob = Would it be unusual to randomly select 9 students from the special programs and get exactly 6 that graduate? O no, it is not unusual O yes, it is unusual If 9 of the students from the special programs are randomly selected, find the probability that at most 6 of them graduated. prob = Would it be unusual to randomly select 9 students from the special programs and get at most 6 that graduate? O yes, it is unusual C) no, it is not unusual Would it be unusual to randomly select 9 students from the special programs and get only 6 that graduate? O no, it is not unusual C) es it is unu u Members of fraternities and sororities are required to volunteer for community service. Do fratemity brothers work fewer volunteer hours on average than sorority sisters? The data below show the number of volunteer hours worked for ten randomly selected fraternity brothers and eleven randomly selected sorority sisters. 11 7 13 8 8 12 Brothers: 4 3 4 11 Sisters: 6 6 17 19 6 16 9 5 9 8 17 Assume both follow a Normal distribution. What can be concluded at the a 0.05 level Of significance level Of significance? For this study, we should use a. The null and alternative hypotheses would be: Ho: select an b. The test statistic (Round intermediate statistics to 1 decimal place. Please show your test statistic to 3 decimal places.) c. The p-value - (Note: If you do not have a Ti83/84, then please use the Google Sheet function Stat),degrees of freedom, tails), where tails is equal to 1 or 2 depending on the test, to report the answer accurate to four decimal places. Use the rounded test statistic value. d. The p-value is a e. Based on this, we should the null hypothesis. f. Thus, the final conclusion is that O The results are statistically significant at a - 0.05, so there is sufficient evidence to conclude that the mean volunteer hours for the ten fraternity brothers that were surveyed is less than the mean volunteer work hours for the eleven sorority sisters that were surveyed. O The results are statistically insignificant at a = 0.05, so there is statistically significant evidence to conclude that the population mean volunteer hours for fraternity brothers is equal to the population mean volunteer work hours for sorority sisters. C) The results are statistically significant at a = 0.05, so there is sufficient evidence to conclude that the population mean volunteer hours for fraternity brothers is less than the population mean volunteer work hours for sorori!y sisters. C) The results are statistically insignificant at a 0.05, so there is insufficient evidence to conclude that the population mean volunteer hours for fraternity brothers is less than the population mean volunteer work hours for sorority sisters.