Below is the statement with information for the questions below. I was hoping someone would be able to double check questions a.-i. As well as helping me figure j.

A standardized visual working memory test has a population mean () of 15 and a standard deviation () of 8. Because the scores are normally distributed, the whole distribution of scores can be converted into a Z distribution. Each raw score in the original distribution has a corresponding Z score in the Z distribution. The Z distribution has symmetrical bell shape with known properties, so it's possible to mathematically figure out the percentage of scores within any specified area in the distribution.

a. John has a score of 13. What is John's Z score?

(2 points total, 1 for process and 1 for process/work.)

Z score = (x-m)/s = (score-mean)/standard deviation

Z= (13-15)/8

Z= -2/8

Z= -.25

b. What is the percentage of students that score lower than John?

P (Z<-.025) = 0.40129

As a percentage, (0.40129 * 100) = 40.129% = 40.13%

c. Based on the Z table, if 1000 students take the test, how many of them would likely score above John's score? (Round the answer to a whole number)

P (13>Z) = .4013 or 40.13%

40.13% of 1000 = 401.3 = 401

d. Tom has a score of 25. What is Tom's Z score?

Z score = (x-m)/s = (score-mean)/standard deviation

Z = (25-15)/8

Z = 10/8

Z = 1.25

e. What is the percentage of students that score lower than Tom?

P (Z < 1.25) = .1056

As a percentage, (.1056 * 100) = 10.56%

f. Based on the Z table, if 1000 students take the test, how many of them would likely score below Tom's score? (Round the answer to a whole number)

P (25

10.56% of 1000 = 105.6 = 106

g. What is the percentage of students that score between John and Tom?

John's Z score is -0.25, located to the left of the mean.

Tom's Z score is 1.25, located to the right of the mean.

To figure the proportion (percentage) of the distribution between Tom and John, we need to find the area between John's score and the mean, plus the area between the mean and Tom's score.

The area between John's Z score and the mean is 40.13%.

The area between Tom's Z score and the mean is 10.56 %.

40.13% + 10.56% = 50.69%

h. Anna scores at the 90^th percentile on this exam, what is her Z score?

Hint: A score at 90^th percentile means 90% of the scores are below this score.

There is 10% above Anna, so Z score can be found by a tail area of 10 % in the Z table. The closest 10% tail area is 10.03%, which corresponds to Z = 1.28

i. Based on the result of the previous question, what is Anna's raw score of working memory?

Anna's Z score is 1.28 = (x-m)/s = (x- mean)/ standard deviationm = 15s = 8

X= 1.28(8) +15= 25.24

j. What would be the median raw score on this exam?