// Numbas version: finer_feedback_settings {"name": "Inverse Normal Distribution (study time or baby weight)", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Inverse Normal Distribution (study time or baby weight)", "tags": [], "metadata": {"description": "

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Given a random variable $X$  normally distributed as $\\operatorname{N}(m,\\sigma^2)$ find probabilities $P(X \\gt a),\\; a \\gt m;\\;\\;P(X \\lt b),\\;b \\lt m$.

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Let $X$ represent the {chosen_amount} of {chosen_stuff}. It is known that $X$ follows a Normal distribution with a mean of {chosen_m} {chosen_units} and a standard deviation of {chosen_s} {chosen_units}.

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If {percentage}% of {chosen_item}s {chosen_verb} less than {x} {chosen_units} then we can write $P(X < x ) = \\var{prob}$

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Using the Standard Normal tables we can write $P(Z < \\var{z1}) = \\var{prob}$

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Now $x = \\mu + z \\times \\sigma$

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so that $x = \\var{chosen_m} + (\\var{z1}\\times \\var{chosen_s})= \\var{x1}$

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{percentage}% of {chosen_item}s {chosen_verb} less than {x} {chosen_units}.
Calculate the value of {x}.

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{x} = [[0]]   

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