I am not sure if I'm doing this correctly and I desperately need help!

Q3. Proportions (percentages) in a Z Distribution (10 points)

A standardized visual working memory test has a population mean () of 58 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 a 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.

-Each question = 1 point: Deduct 0.5 if the calculation process is correct but the result is wrong

Helpful tips:

To answer the following questions, it helps to draw a Z distribution (bell curve) and place an individual's Z score on the distribution as a visual aid. Use the Z table for converting between Z score and area (percentage) of the distribution marked by this Z score.

a. Ramone has a score of 52. What is Ramone's Z score? Round the result to the hundredth (2^nd place to the right of the decimal).

=Z = = = Z score = -0.75or if we are following the rules of the Z table which has no negatives, the answer would be 0.75.

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

P=100 (Z <- 0.75) = 100( 0.5-0.2734) = 100 * .2266= 22.66%scored lower than Ramone.

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

Area above Z = 0.75 is 27.34 + 50= 77.34 * 10 (1000 students) = 773.4 rounded to 773 students likely to score above Ramone.

d. Ezra has a score of 78. What is Ezra's Z score?

=Z = = = 2.5

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

P= 100 (Z < 2.5) = 100 (0.5 + 0.4938) = 100* .9938= 99.38%

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

1000* P ( Z <78) = 1000* 0.9938 = 993.80 rounded to 994 students.

g. What is the percentage of students that score between Ramone and Ezra?

100(P(-0.75

h. Jess scores at the 86^th percentile on this exam, what is her Z score?

Hint: A score at 86^th percentile means 86% of the scores are below this score.

If Jess scored in the 86% she scored .86 above the rest of the class. According to the Z table that comes at toZ= 1.08

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

Z= 1.08 = = 1.8*8=14.4. X = 58+14.4= raw score =72.4

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

Hint: Review the definition of "median" and then figure out the percentage of scores below (or above) this score.

The. Median raw score is 58. Since for normal distribution mean= median