Question

Application for n.. Google Translate Apps Q Spring Stat 3000/8000 course Homework: Chapter 5 Homewo Score: 0 of 1 pt 51.50-T Some IQ tests are standardized to a Normal model N(100,19). a) What cutoff value bounds the highest 10% of all IQs? b) What cutoff value bounds the lowest 25% of the IQs? c) What cutoff values bound the middle 60% of the IQs? a) The cutoff value is 124.3 Round to one decimal place as needed.) b) The cutoff value is 112.9 Round to one decimal place as needed.) Enter your answer in the answer box and then click Check Answer. part remaining

Answer 1

solution:-
given that mean = 100 , standard deviation = 19

a.the highest 10% is 1.28
then formula
=> z = (x - μ)/σ
=> x = μ + z*σ
x = 100 + 1.28 * 19
x = 124.3

b.the lowest 25% i -0.67
then formula
=> z = (x - μ)/σ
=> x = μ + z*σ
x = 100 +(-0.67) * 19
x = 87.3

c.the cutoff value bound the middle 60% is
=> (1 - 0.60)/2 = 0.40/2 = 0.20

the middle value of 60% is -0.84 and 0.84
=> z1 = (x1 - μ1)/σ1
=> x1 = μ1 + z1*σ1
x1 = 100 +(-0.84)* 19
x1 = 84.0

and z2 = (x2 - μ2)/σ2
=> x2 = μ2 + z2*σ2
x2 = 100 + 0.84* 19
x2 = 116.0

the cutoff values are 84.0 and 116.0