Question

The heights of 13-year-old girls are normal distribution with mean 62.6 inches and a standard deviation of 7.2 inches. Erin is taller than 80% of the girls her age. How tall is Erin?

A researcher wishes to use students' IQ 's to predict their SAT. There is a correlation of 0.82 between SAT scores and IQ scores. The average SAT verbal score is 500, with a standard deviation of 100. The average IQ score is 100 with a standard deviation of 15.

Calculate the equation for the least-squares regression line

Answer 1

Question 1

The heights of 13-year-old girls are normal distribution with mean 62.6 inches and a standard deviation of 7.2 inches. Erin is taller than 80% of the girls her age. How tall is Erin?

Solution:

We are given

µ = 62.6

σ = 7.2

Z-score for 80% of below scores by using z-table or excel is given as below:

Z = 0.841621

Erin’s height = X = µ + Z*σ = 62.6 + 0.841621*7.2 = 68.65967

Erin’s height = 68.66 inch

Question 2

A researcher wishes to use students' IQ 's to predict their SAT. There is a correlation of 0.82 between SAT scores and IQ scores. The average SAT verbal score is 500, with a standard deviation of 100. The average IQ score is 100 with a standard deviation of 15.

Calculate the equation for the least-squares regression line

Solution:

We are given

r = 0.82

Sy = 100

Sx = 15

Ybar = 500

Xbar = 100

b = r*Sy/Sx

b = 0.82*100/15

b = 5.466667

a = Ybar – b*Xbar

a = 500 - 5.466667*100

a = -46.6667

The regression equation is given as below:

y = a + bx

y = -46.6667 + 5.466667*x