Question

1. Normal distribution (15 points)

Below are summary statistics for the subset of Asian applicants.

What fraction of people have incomes between $50 thousand and $150 thousand under the assumption that the income data follow a normal distribution?

asian <-subset(exam, exam$Race=="Asian")
sum(!is.na(asian$ApplicantIncome))  #Sample size

1095

mean(asian$ApplicantIncome)         #Sample mean

120

SD(asian$ApplicantIncome)           #Sample std deviation

78

Answer 1

Let X is Income and X is normal with

mean=m=120

standard deviation =SD=78

we have to find P(50<X<150)

so 46.5% of peoples have income between 50 and 150