Question

1. Please explain why you would or would not think each of the following variables to be normally distributed. [Hint: For normally distributed variable, most of the data are around the middle value and frequency of observations keeps falling as you move away from the middle in both directions]. a. Retirement age of the U.S workers. b. Household income in the U.S. in 2018. c. Height of U.S. adults in 2018. d. Birthweight of girls in the U.S. in 2018. e. Please state an example each of left-skewed and right-skewed variables and justify your answer.

Answer 1

Question 1

(a) Here retirement age of the US workers will not be normally distributed. As most of the people retirement after a certain age and it may have a high peak like 65 years and then a downward distribution. Not symmetric in any sense.

(b) Household income in the US in 2018 would be a rightly skewed disribution. So, that would not be a normal distribution.

(c) House of US adults in 2018 can be assumed as normal distribution as there is an average height and there are data around the middle values and frequency reduced alongside like extra heighted people and some midgets.

(d) Here birthweight of girl in the US can also be assumed as normal distribution as here there is an average weight, where birthweight of most of the girls lies and then some are underweight and some are overweight.

(e) Here example of left skewed variable is GPA of an university students. as the highest number of frequency of people has GPA around 3 to 3.4 but it can maximum go to 4 and very less people can get 4, and similarly very less people can get 1 or 2 GPA and it is increasing and maxed out at 3 to 3.5

Now positive skewed variable is household income, as it can go to very high but frequency of that is very less. and most of the people as are in middle class and lower income there is high frequency on lower side of the horizontal axis.