3. A common criticism of the U.S. Senate is that the age of the senators does not accurately reflect the current population. The mean age of the population of current senators is 63.6 years. The population standard deviation is 10.4 years (data from Wiki). In January 2021, the state of Georgia held run-off elections for both senate positions and both resulted in noteworthy, history-making outcomes. Jon Ossoff was sworn into office a month before his 34^th birthday and is the first person of Jewish descent elected as senator in Georgia. Rev. Raphael Warnock was 51 years old and is the first African American elected as senator in Georgia . (C7 and 8). Round z-score two decimal places and probabilities four decimal places.

a)What is the z-score that represents Ossoff's age of 34? Is it unusual?

b)What is the z-score that represents Warnock's age of 51? Is it unusual?

c)If you were to select one senator at random, what is the probability that they would be under the age of 55?

d)If you select 20 senators at random, what is the probability that they would be under the age of 55?

e)Think about it: 13 current senators began serving as senators before the year 2000. Three are women, 10 are men, and all 13 are White. They have a mean age of 77 and a sample standard deviation of 7.6. Given your findings, would you recommend setting term limits? Why or why not?