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NSWMaths Standard 2Quick questions
Year 12: Statistical Analysis
Quick questions on The normal distribution and the empirical rule for HSC Maths Standard 2
11short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is the normal distribution?Show answer
The normal distribution (or bell curve) is a continuous probability distribution that arises naturally in many contexts (heights, exam scores, measurement errors, manufacturing variation). Its shape is fully specified by two parameters:
What is the empirical rule (68-95-99.7)?Show answer
By symmetry, the tails (one side) are half the outside-the-band amount:
What is common standard-deviation regions?Show answer
These add up: from the mean to the right tail.
What is applying the rule?Show answer
To find the percentage of data in some range:
What is when the normal distribution applies?Show answer
The normal distribution is the default model whenever a quantity is the result of many small, independent influences adding up.
What is australian manufacturing context?Show answer
A bottling factory fills mL drink bottles with mean mL and standard deviation mL. Bottles with less than mL would fail quality control.
What is two-sided interval?Show answer
Heights of Year 12 girls at an Australian school are approximately normally distributed with mean cm and standard deviation cm.
What is forgetting to halve?Show answer
"Above SD" is , not . The is both tails combined.
What is using the rule for non-normal data?Show answer
The empirical rule only applies when the data is approximately normally distributed.
What is standard deviation vs variance?Show answer
The empirical rule uses standard deviation , not variance .
What is treating endpoints exactly?Show answer
The empirical rule percentages are approximations: is really , is , is . The rounded values are fine for Standard 2. :::