Chapter 6 Normal Distributions The normal distribution is a probability function that describes how the values of a variable are distributed It is an asymmetric distribution where most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions Extreme values in both tails of the distribution are similarly unlikely (Frost, 2021) In the next two scenarios, you will use the properties of normal distributions to examine the data Age of Senators 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 Round z score two decimal places and probabilities four decimal places What is the z score that represents Ossoff's age of 34 Is it unusual What is the z score that represents Warnock's age of 51 Is it unusual If you were to select one senator at random, what is the probability that they would be under the age of 55 (you will need to find another z score) If you select 20 senators at random, what is the probability that they would be under the age of 55 Thirteen 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 SAT Scores SAT scores have long been associated with household income The mean score for all SAT test takers in 2018 nationwide was 1068, but NC test takers had a mean of 1098, with a standard deviation of 183 Given that NC students had a mean SAT score was 1098 with a standard deviation of 183 If a student in NC scored 1068, what would their z score be In NC, the mean SAT score was 1098 with a standard deviation of 183 A student who did NOT receive a fee waiver (aka had to pay to take the SAT) in NC scored an average of 1141 If a student in NC scored 1141, what would their z score be What percentage of students in NC scored between 1068 and 1141 Write a decimal rounded 4 decimal places UNC Chapel Hill is the oldest (and often ranked the best) public college in the U S and is highly competitive For an above average chance of being selected for admission, you need to score in the Top 2 of NC test takers What score do you need to be competitive for UNC Chapel Hill to the nearest whole point

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Chapter 6: Normal Distributions The normal distribution is a probability function that describes how the values of a variable are distributed. It is an asymmetric

Chapter 6: Normal Distributions

"The normal distribution is a probability function that describes how the values of a variable are distributed. It is an asymmetric distribution where most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions. Extreme values in both tails of the distribution are similarly unlikely" (Frost, 2021). In the next two scenarios, you will use the properties of normal distributions to examine the data.

Age of Senators

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. Round z-score two decimal places and probabilities four decimal places.

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

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

If you were to select one senator at random, what is the probability that they would be under the age of 55 (you will need to find another z-score)?

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

Thirteen 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?

SAT Scores

SAT scores have long been associated with household income. The mean score for all SAT test-takers in 2018 nationwide was 1068, but NC test-takers had a mean of 1098, with a standard deviation of 183.

Given that NC students had a mean SAT score was 1098 with a standard deviation of 183. If a student in NC scored 1068, what would their z-score be?

In NC, the mean SAT score was 1098 with a standard deviation of 183. A student who did NOT receive a fee waiver (aka - had to pay to take the SAT) in NC scored an average of 1141. If a student in NC scored 1141, what would their z-score be?

What percentage of students in NC scored between 1068 and 1141? Write a decimal rounded 4 decimal places.

UNC-Chapel Hill is the oldest (and often ranked the best) public college in the U.S. and is highly competitive. For an "above average" chance of being selected for admission, you need to score in the Top 2% of NC test takers. What score do you need to be competitive for UNC-Chapel Hill to the nearest whole point?