Continuous random variable and normal distribution
Continuous random variables and the normal distribution for IB Applications SL: GDC probabilities, inverse calculations and worked IB exam questions.
When a variable can take any value in an interval (height, weight, time), probability is calculated as an area under a curve, and the probability of an exact value is zero. The most important curve is the bell of the normal distribution , which describes heights, weights, measurement errors and many real quantities. In the IB exam almost everything is done with the graphic display calculator: calculating a probability given the limits, or the reverse, finding the value that leaves a given probability. The decisive thing is to draw the bell and shade the area you are asked about before typing anything.
Recommended order
Follow the sections in order: continuous random variable and density function, the normal distribution and normal calculations. At the end you have the IB exam questions grouped by type.
Discrete random variable and binomial distribution (topic 11).
Sections in this topic
Continuous random variable and density function
What a continuous random variable is, what a density function is, and why a probability is an area under the curve. IB Applications SL.
3 worked examples Section 2The normal distribution: mean, standard deviation and standardisation
What the normal distribution N(μ, σ) is, how its bell curve looks, the 68-95-99.7 rule and how to standardise with z. Worked IB Applications SL examples.
3 worked examples Section 3Normal distribution calculations: probabilities and inverse values
How to calculate normal probabilities and inverse values with the GDC, find the mean or standard deviation and solve context problems. IB Applications SL.
3 worked examples End of topicIB exam questions for topic 12
IB exam questions on the normal distribution: probabilities, inverse normal, finding the mean or standard deviation, with step-by-step solutions.
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