Normal distribution Practice

{"questions":[{"content":"Fluency: if variance is 25, the standard deviation is [[input-nor-t1]]","widgets":{"input-nor-t1":{"type":"input","answer":"5"}},"hints":["Take the positive square root."],"explanation":"σ = √25 = 5."},{"content":"Method recognition: the lowest 8% boundary is requested. Choose the operation.<br>[[choice-nor-t2]]","widgets":{"choice-nor-t2":{"type":"choice","options":["Inverse normal","Normal CDF only","Regression","Numerical integration"],"answer":[0],"explanations":["Use inverse normal with left-tail area 0.08.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again."]}},"hints":["An area is known and a value is unknown."],"explanation":"Use inverse normal with left-tail area 0.08."},{"content":"Exam execution: which line should appear before calculator output?<br>[[choice-nor-t3]]","widgets":{"choice-nor-t3":{"type":"choice","options":["X ~ N(μ, σ²) and the required probability","Only the final decimal","The calculator model number","A list of button presses"],"answer":[0],"explanations":["The distribution and event justify the operation.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again."]}},"hints":["Communicate the mathematical setup."],"explanation":"The distribution and event justify the operation."},{"content":"Synthesis: P(X > a) = 0.12. Which left-tail area is entered for inverse normal?<br>[[choice-nor-t4]]","widgets":{"choice-nor-t4":{"type":"choice","options":["0.88","0.12","1.12","−0.12"],"answer":[0],"explanations":["P(X < a) = 1 − 0.12 = 0.88.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again."]}},"hints":["Convert a right tail to the area below."],"explanation":"P(X < a) = 1 − 0.12 = 0.88."},{"content":"What should you do next after translating “between 45 and 60” into bounds?<br>[[choice-nor-t5]]","widgets":{"choice-nor-t5":{"type":"choice","options":["Use normal CDF and interpret the resulting area","Use inverse normal","Differentiate the density","Apply induction"],"answer":[0],"explanations":["Normal CDF evaluates the probability between known bounds.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again.","Check the mathematical conditions and try again."]}},"hints":["Both boundaries are known."],"explanation":"Normal CDF evaluates the probability between known bounds."}],"mix":1}