Question

Show your work CLEARLY and COMPLETELY! For z-scores: Round to the SECOND decimal place. For Probabilities: Keep the Original FOUR decimal places. For EACH part of the question: Draw a Normal Curve and highlight the corresponding area(s)! Name: Problem 1 Stanford-Binet lQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 16. Find the probability that a randomly selected person has an IQ test score a) Over 130. Answer Canvas Quiz 5-1 and 5-2. (2 points) b) Under 85. Answer Canvas Quiz 5-3 and 5-4. (2 points) c) Between 72 and 128. Answer Canvas Quiz 5-5 to 5-7. (3 points) d) Between+1.25 standard deviations of the mean. Answer Canvas Quiz 5-8. (1 point)

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	100
std deviation   =σ=	16.0000

probability =

P(X>130)

=

P(Z>1.88)=

1-P(Z<1.88)=

1-0.9699=

0.0301

b)

probability =

P(X<85)

=

P(Z<-0.94)=

0.1736

c)

probability =

P(72<X<128)

=

P(-1.75<Z<1.75)=

0.9599-0.0401=

0.9198

d)

P(-1.25<Z<1.25)=0.8944-0.1056=0.7888

2)

mean μ=	40000
standard deviation σ=	4000.0000

for 3th percentile critical value of z=		-1.88
therefore corresponding value=mean+z*std deviation=			32480.0