Question

What proportion of a normal distribution is located between each of the following Z-score boundaries?

 a. z= -0.50 and z= +0.50

 b. z=-0.90 and z= +0.90

 c. z=-1.50 and z= 1.50 

For a normal distribution with a mean of μ = 80 and a standard deviation of σ= 20, find the proportion of the population corresponding to each of the following.

 a. Scores greater than 85.

 b. Scores less than 100.

 c. Scores between 70 and 90. 

IQ test scores are standardized to produce a normal distribution with a mean of μ = 100 and a standard deviation of σ = 15. Find the proportion of the population in each of the following IQ categories.

 a. Genius or near genius: IQ greater than 140

 b. Very smartypants: IQ between 120 and 140

 c. Average or normal intelligence: IQ between 90 and 109. 

The distribution of SAT scores is normal with μ = 500 and σ= 100. 

a. What SAT score, X value, separates the top 15% of the distribution from the rest? 

b. What SAT score, X value, separates the top 10% of the distribution from the rest? 

c. SAT score, X value, separates the top 2% of the distribution from the rest?

Answer 1

solution: - a) P(-0.50 cze 0-50) P[200.50) Plze-0.50) - 0.6915 -0. 3085 - こ 0.3830 b) P(-0.go = L22 0.go) Plzco.go) PlZ2-0.90) tool 0.8159 o.1841 0.6318 Pl-1.5c72105)= Pla21:50) - - P/22-2.50) = 0.9332-0.0668 – 10.8664 2) Z=x-Y e li = 80 o=20 a) P(x>85) = P12385-40) - P(Z > 0.25) - 0.4013 Plze b) plxcroo) 100-80) Plzel) 20 = 0.8413 go-so - 20 o P(702XC 90) Pl 70-80 cze P(-0.5c720.5) = 0-3830