// Numbas version: finer_feedback_settings {"name": "MSS - Normal Distribution Area Left", "extensions": ["stats", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "MSS - Normal Distribution Area Left", "tags": ["Normal distribution", "normal distribution", "statistics"], "metadata": {"description": "

Students are asked to move an x-axis slider on a normal distribution to make the area to the left of the slider equal to a certain percentage. The 6 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

The graph below displays a standard normal distribution.

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The rules of thumb for the normal distribution show that:

the area between $-1$ and $+1$ standard deviations is approximately $68$%.

This means that the area between the mean and $-1$ standard deviation is approximately $34$%,

and the area between the left edge of the graph and $-1$ standard deviation is approximately $50-34$% = $16$%.

The area between the mean and $+1$ standard deviation is approximately $34$%,

and the area between the left edge of the graph and $+1$ standard deviation is approximately $50+34$% = $84$%.

the area between $-2$ and $+2$ standard deviations is approximately $95$%.

This means that the area between the mean and $-2$ standard deviations is approximately $47.5$%,

and the area between the left edge of the graph and $-2$ standard deviations is approximately $50-47.5$% = $2.5$%.

The area between the mean and $+2$ standard deviations is approximately $47.5$%,

and the area between the left edge of the graph and $+2$ standard deviations is approximately $50+47.5$% = $97.5$%.

the area between $-3$ and $+3$ standard deviations is approximately $99.7$%.

This means that the area between the mean and $-3$ standard deviations is approximately $49.85$%,

and the area between the left edge of the graph and $-3$ standard deviations is approximately $50-49.85$% = $0.15$%.

The area between the mean and $+3$ standard deviations is approximately $49.85$%,

and the area between the left edge of the graph and $+3$ standard deviations is approximately $50+49.85$% = $99.85$%.

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P(z<=Z)

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Adjust the slider so that the shaded area under the curve is equal to approximately $\\var{question_areapercentage}$% of the total area under the curve.

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