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.

AFDA.DA.4.b

Determine when the normal distribution is a reasonable representation of the data.

Example Problems

Talia designed a spinner divided into seven equal segments. She spun it 350 times and recorded how often each segment was hit.

Segment	1	2	3	4	5	6	7
Observed hits	52	46	53	45	47	54	53

Talia wants to perform a

\chi^2

goodness-of-fit test to determine if these results suggest that the spinner lands on one specific segment more often than the others.

What is the expected count of hits for segment 5?

Olivia coordinates wildlife observations across six hiking trails and wonders if sightings are equally likely on each trail. In a sample of 415 sightings, she recorded:

Trail	A	B	C	D	E	F
Sightings	66	70	63	68	73	75

Olivia wants to perform a χ² goodness-of-fit test to determine if these results suggest that one trail receives more sightings than the others.

What is the expected count of sightings on Trail F?
Round your answer to the nearest hundredth.

Arturo manages baggage flow at an airport with five carousels, intended to receive equal shares of bags. He samples one period and records:

Carousel	1	2	3	4	5	Total
Expected	20%	20%	20%	20%	20%	100%
Bags observed	185	195	190	190	190	950

Arturo wants to perform a χ² goodness-of-fit test to determine if these results suggest that the bags are not evenly distributed.

What is the expected count of bags on carousel 4?

Khan Academy Resources

Qualitative sense of normal distributions

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