Question

Before analyzing the data for relationships, the school counselor decides that he should first look at the population parameters of the SAT scores. he finds that the population of SAT scores. he finds that the population of SAT scores is normally distributed with a mean of 500 and a standard deviation of 100.

1. Draw this theoretical population, scale the x-axis in raw SAT scores, and provide demaraction lines (vertical dotted lines) where -2,-1,0,+2 Z-scores would fall. indicate the relative proportion of data that fall between each z-score, including the proportion of data +/-2.

2.provide the z-scores for a) x=500, b)x=530, c)x=470.

3.provide the raw scores for z=-2.1, z=+.85, and z=0

4.provide the raw scores for the 5th, 50th, and 95th percentiles.

5. give the probability that a randomly selected score would:

a. Fall at x=500 or below

b. Fall at 530 or above

c. Fall at or below 470

d. Fall at or above 380

e. Fall at or below z=0

f. Fall at or above z=-2.1

g. Fall at or above z=+.85

Answer 1

Given that mean =500 and standard deviation as 100

HenHe.

1.

2.z score at x=500.

Again at x=530

At x=470

3.raw score at Z =-2.1

At Z=.85

At Z=0

4. To find raw score percentile 5th percentile we need to find it through Z score table need to see 0.05 area and find the z score corrospondingcto it and hence calculate the raw data

So, Z score corresponding to 5th percentile -1.645

Hence x=500- 164.5= 335.5

Again at 50th percentile as the median since it is normal distribution hence X at 50th percentile is 500

Again at 95th percentile see the table we get

Z= +1.645 hence x=500+ 164.5= 664.5

5. a) To find the probability below x=500

Z ascoreasat x=500 is 0 hence probaility is 0.50

b) above x=530 z score at 530 is +0.3 hence seeing area above z=0.3 at table is 1-0.6179=0.3821

c) z score at x=470 .

Z=-0.3

Probaility as 0.3821

D. Z at x=380

Z=-1.20, Probability= 1-0.1151=0.8849

E. Area fall below z=0 is 0.50 by table

F. Area fall above z=-2.1 as 1-0.0179=0.9821

G.area above z= +0.85 as 1-0.8023=0.1977