Question

a) What is the adult male height at 80 %? where the mean height is 73 inches and the standard deviation is 3.3.

b) What is the score of Jake at 37 %? if the SAT (μ =1500, σ =300).

c) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x-score that corresponds to a z-score of 2.33.

Answer 1

a)

u = 73

s = 3.3

From percentile to z score calculator

Z = 0.8416( Corresponding to 80%)

Z = (X - u )/ s

0.8416 = ( X - 73 ) /3.3

X = 73 + 3.3*0.8416

X =75.7773

b) From percentile to z score calculator

Z = -0.3319 ( Corresponding to 37%)

u = 1500

s = 300

Z = (X - u )/ s

-0.3319 = ( X -1500)/300

X = 1500 + 300(-0.3319)

X = 1400.43

c)

Z = 2.33

u = 100

s = 15

Z = (X - u )/ s

2.33 = ( X - 100 ) /15

X = 100 + 15*2.33

X = 134.95