Normal distribution
Practice Flashcards
What does X ~ N(μ, σ²) mean?
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All Flashcards in Topic 4.9
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4.9.19 cards
What does X ~ N(μ, σ²) mean?
X is normally distributed with mean μ and variance σ² (so standard deviation σ).
What shape is the normal distribution?
A symmetric bell curve centred on the mean.
What does normalcdf(lower, upper, μ, σ) give?
The probability P(lower < X < upper) — the area under the curve between the bounds.
How do you find P(X < a) on the GDC?
normalcdf with a very small lower bound (e.g. −1E99) and upper bound a.
How do you find P(X > a)?
normalcdf with lower bound a and a very large upper bound (e.g. 1E99).
What is P(X < μ)?
0.5 — half the area is below the mean.
State the 68–95–99.7 rule.
About 68% of data lies within 1σ of the mean, 95% within 2σ, 99.7% within 3σ.
How do you find an expected number from a normal probability?
Multiply the probability (normalcdf) by the total number of items.
In N(150, 20²), what is σ?
20 (the variance is 400; the GDC needs σ = 20).
4.9.29 cards
What shape is the normal distribution?
A symmetric bell curve centred on the mean.
For a normal curve, how do the mean, median and mode compare?
They are all equal (by symmetry).
What is the total area under a normal curve?
1.
What is P(X < μ) for a normal distribution?
0.5 — half the area lies below the mean.
How is a probability shown on a normal-curve sketch?
As the area of the shaded region.
What happens to the curve if the mean increases (σ fixed)?
It shifts to the right, keeping the same shape.
What happens if σ increases (mean fixed)?
The curve becomes wider and flatter (more spread).
What does a smaller σ mean for the data?
The values are more clustered / consistent (taller, narrower curve).
By symmetry, P(X > μ + σ) equals which left-tail probability?
P(X < μ − σ) — symmetric tails are equal.
Topic 4.9 study notes
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