Please help me understand this concept. I need explanations on how…

Question Answered step-by-step Please help me understand this concept. I need explanations on how… Please help me understand this concept. I need explanations on how do these. thank you   Q3. Proportions (percentages) in a Z Distribution [10 points]A standardized visual working memory test has a population mean (?) of 54 and a standard deviation (?) of 4. 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. 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  Use this Normal Distribution Table to visualize how your z scores are plotted on a normal distribution:  https://www.mathsisfun.com/data/standard-normal-distribution-table.html .  Q3 A. Raven has a score of 47. What is Raven’s Z score? Round the result to the hundredth (2nd place to the right of the decimal).[1 point] Z = (X-m)/s*Population Mean = m*Population Standard Deviation = s*Raw Score = X*Z score = ZZ= (X-M)/SD Z= (47 – 54)/4 Z= -7/4 Z= -1.75    Q3 B. What is the percentage of students that score lower than Raven?[1 point]  Q3 C. Based on the Z table, if 1000 students take the test, how many of them would likely score above Raven’s score? (Round the answer to a whole number)[1 point]  Q3 D. Erica has a score of 59. What is Erica’s Z score? [1 point] Z = (X-m)/s*Population Mean = m*Population Standard Deviation = s*Raw Score = X*Z score = ZZ= (X-M)/SD Z= (59 -54)/4 Z= 5/4 Z= 1.25   Q3 E. What is the percentage of students that score lower than Erica?[1 point] Using the standard deviation table 0 to 1.25 is 39.44%. Each side of the table is 50%. So 50% add 39.44 and you can see everyone bellow that point.  39.44+ 50= 89.44% of people score lower than Erica P= = 0.894   Q3 F. Based on the Z table, if 1000 students take the test, how many of them would likely score below Erica’s score? (Round the answer to a whole number)[1 point]    Q3 G. What is the percentage of students that score between Raven and Erica?[1 point]   Q3 H. Ryan scores at the 78th percentile on this exam, what is his Z score?Hint: A score at 78th percentile means 78% of the scores are below this score.[1 point]   Q3 I. Based on the result of the previous question and using the population mean and SD for Q3, what is Ryan’s raw score of working memory?[1 point]  Q3 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.[1 point]       Q4. Z Distribution: From Probabilities to Proportions (percentages) [7 points]Answer the following questions with this scenario:A school district runs a gifted language program in fourth grade with a selection criterion of 97th percentile. That is, students who score at 97th percentile or above on a standardized language test are eligible for the gifted program. Answer the following question based on this scenario. Helpful tips:Review the tutorial videos on “how to use the Z table” before answering the following questions. Image transcription text97%… Show more Q4 A. What is the probability of randomly drawing a student from the whole population of fourth-graders that would meet the selection criterion for the gifted program? [1 point] Both the answer and the rationale must be correct to earn the credit   Q4 B. If the district has 321 fourth-graders in total, how many will be eligible for the gifted program? [1 point] Deduct .5 if the process is correct but the result was calculated incorrectly   Q4 C. If we use a Z distribution to represent all the test scores from the fourth-graders, what is the Z score that serves as the critical (or cutoff) value for determining eligibility for the gifted program? [2 points] Both the answer and the rationale must be correct to earn the credit.  Q4 D. This standardized test used for the screening process has a published raw score mean (?) of 88 and standard deviation (?) of 3. Based on the critical Z score (from question c above, what would be the critical test score if we use the original raw scores to determine the students’ eligibility?[1 point] Deduct .5 if the process is correct but the result was calculated incorrectly   Q4 E. Casey has a raw score of 94, is she eligible for the gifted program? Explain your rationale for this answer. [1 point] Both the answer and the rationale must be correct to earn the credit   Q4 F. Phillip has a Z score of -2.5, is he eligible for the gifted program? [1 point] Both the answer and the rationale must be correct to earn the credit     Q5. Z Distribution: From Probabilities to Proportions [7 points]Answer the following questions with this scenario:In a health initiative, the local school district would like to promote awareness of the students’ BMI (body mass index) and encourage parents of students with extremely high or extremely low BMI to work with the school nurse in improving their children’s health. The school district decides to measure all third-graders’ BMIs, identify the highest 1% and the lowest 1% of the students, and then follow up with their parents. The graph below demonstrates the areas in the BMI distribution for the health program. Helpful tips:Review the tutorial videos on “how to use the Z table” before answering the following questions. Image transcription text1% 1%… Show more Q5A. If we randomly draw one third-grader out of the school district, what is the probability of that child having a BMI that meets the criterion for the health program? Explain how you figure out the answer. [1 point] Both the answer and the rationale must be correct to earn the credit  Q5B. If the BMI distribution is converted into a Z distribution, what would be the upper critical Z value and the lower critical Z value that mark the two “significant” areas at the tails? [2 points] 1 point for each critical Z   1. Explain how you found the answers. [1 point]  Q5C. If Shelby’s BMI is converted into a Z score of -2.30, is Shelby included in the health follow-up program? Explain your rationale for this answer.[1 point] Both the answer and the rationale must be correct to earn the credit   Q5D. If the school district has a total of 3,540 third-graders, how many students’ parents will be contacted by the school nurse? (Round the answer to a whole number) [1 point] .5 if the process is correct but the result was calculated incorrectly   Q5E. If the school district chooses a different strategy and sets the higher and lower cut-off points at Z values of +2.28 and -2.28, will the school nurse have more students or fewer students to follow up with, compared to the original cut-offs (1% at the upper and lower ends of the distribution)? 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