Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 25 minutes, as an unvalidated planning estimate. This collection contains 2 tasks; choose a manageable set and return for further sessions. Completing the whole collection may take substantially longer. This is a unit assessment, not a full course or AP examination.
Write the event and distribution assumptions before using the calculator.
Record inputs and enough intermediate precision to verify the final rounded answer.
The public solutions support review; completing a tool query does not establish mastery.
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0 of 2 tasks have recorded responses. No overall mastery score is assigned.
A stipulated process produces 25 independent binary outcomes, each with success probability 0.16. Calculate P(X>5), give the complementary lower-tail query, and check the result by summing the point probabilities for 6 through 25. A colleague instead stops collecting as soon as the fifth success occurs. Explain why the same fixed-n binomial question does not describe the colleague’s stopping time.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
A normal measurement model has mean 50 centimeters and standard deviation 6 centimeters. Find (a) the cutoff exceeded by 5% and (b) both endpoints of the central 95% interval. Verify the probabilities with forward queries. Explain why the upper endpoint in(b) differs from(a), then calculate the probability outside interval(b).
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Review and revisit
Use each rubric to identify a valid argument, a missing condition or a step to revise. For independent evaluation, ask a teacher or reviewer to examine the complete reasoning. Self-review and recorded responses are not verified assessment results.
Coverage and targeted lesson returns
A stipulated process produces 25 independent binary outcomes, each with success probability 0.16. Calculate P(X>5), give the complementary lower-tail query, and check the result by summing the point probabilities for 6 through 25. A colleague instead stops collecting as soon as the fifth success occurs. Explain why the same fixed-n binomial question does not describe the colleague’s stopping time.
A normal measurement model has mean 50 centimeters and standard deviation 6 centimeters. Find (a) the cutoff exceeded by 5% and (b) both endpoints of the central 95% interval. Verify the probabilities with forward queries. Explain why the upper endpoint in(b) differs from(a), then calculate the probability outside interval(b).
