Is Goblins free for teachers?

Yes. Goblins offers a generous free tier that includes 1 live feedback assignment per week, insights on student mastery and replays, and the ability to upload your own content. The Max plan adds unlimited assignments, superadaptive mode, grade exports, standards growth reports, and SSO/LMS integration, with per-student pricing for schools and districts.

How does Goblins work?

Three simple steps: (1) Share an assignment from thousands of standards-aligned topics using a share code. (2) Students speak and draw their thinking naturally, and Goblins responds with Socratic questioning that sounds just like their teacher. (3) Teachers get real-time formative insights showing what students struggle with and suggestions to inform instruction.

Does Goblins prevent cheating?

Yes. Goblins uses a purpose-trained AI model that evaluates cheating signals in real time. It can detect when students are copying answers, using external tools inappropriately, or not genuinely working through problems. Copy-pasting answers is also blocked.

Can I use my own voice with Goblins?

Yes. Teachers can record their voice and take a selfie to create a custom 3D avatar in about 30 seconds. Students then hear help in their own teacher's voice and see a familiar face, making the experience more personal and effective.

What math levels does Goblins cover?

Goblins covers math from Grade 5 through AP Calculus, including thousands of standards-aligned topics. Teachers can also upload their own content for custom assignments at any level.

Is Goblins FERPA compliant?

Yes. Goblins is FERPA and state compliant. Student data privacy and security are a top priority.

Does Goblins support English Language Learners?

Yes. Goblins supports 30+ languages so teachers don't have to translate every worksheet. It is especially helpful for ELL students who need accessible math instruction in their native language.

A2.32.a

Verify that a sampling distribution is centered at the population mean and approximately normal if the sample size is large enough.

Example Problems

A farmers' market manager says that 70% of vendors accept credit or debit cards. Suppose that we took random samples of

n = 12

vendors from this population and computed the proportion

\hat{p}

of vendors in each sample who accepted cards. We can assume the manager's claim is true.

What will be the shape of the sampling distribution of

\hat{p}

: skewed to the left, skewed to the right, approximately normal, or uniform?

A national survey suggests that 12% of adults are left-handed. Suppose that we took random samples of

n = 100

adults from this population and computed the proportion

\hat{p}

of adults in each sample who were left-handed. We can assume the survey's claim is true.

What will be the shape of the sampling distribution of

\hat{p}

: skewed to the left, skewed to the right, approximately normal, or uniform?

A local gym reports that 80% of active members check in at least once per week. Suppose that we took random samples of

n = 60

members from this population and computed the proportion

\hat{p}

of members in each sample who checked in at least once that week. We can assume the gym's claim is true.

What will be the shape of the sampling distribution of

\hat{p}

: skewed to the left, skewed to the right, approximately normal, or uniform?

Khan Academy Resources

Basic normal calculations Empirical rule Calculating z-scores Normal distribution: Area between two points Normal distribution: Area above or below a point Normal calculations in reverse Calculate percentiles Qualitative sense of normal distributions Normal distribution problems: Empirical rule Calculating percentile Comparing with z-scores Finding z-score for a percentile Standard normal table for proportion above Standard normal table for proportion between values Standard normal table for proportion below Z-score introduction Threshold for low percentile

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