z-values & inverse normal
Practice Flashcards
State the standardising formula.
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All Flashcards in Topic 4.12
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4.12.19 cards
State the standardising formula.
z = (x − μ)/σ.
What does a z-value tell you?
How many standard deviations x is above (z > 0) or below (z < 0) the mean.
What does z = 0 mean?
The value equals the mean.
What does a negative z-value indicate?
The value is below the mean.
Why are z-values useful for comparing?
They put values from different normal distributions on a common (standardised) scale.
Across two distributions, which result is relatively better?
The one with the larger z-value (further above its own mean).
What is the standard normal distribution?
Z ~ N(0, 1) — mean 0 and standard deviation 1.
Does a z-value have units?
No — it is a count of standard deviations, so it is unitless.
x is 2σ above the mean. What is z?
z = 2.
4.12.29 cards
What does the inverse normal do?
Given a left-tail probability P(X < x), it returns the value x.
What GDC command finds x from a probability?
invNorm(area, μ, σ), where area is the left-tail probability.
Which tail does invNorm use?
The left (lower) tail — the area to the left of x.
How do you find x when P(X > x) = p?
Use the left area 1 − p: x = invNorm(1 − p, μ, σ).
For the central c% of data, what are the tail areas?
Each tail is (1 − c)/2; use those areas in invNorm.
How do you find an unknown σ from a probability?
Find z = invNorm(p, 0, 1), then σ = (x − μ)/z.
How do you find an unknown μ from a probability?
Find z = invNorm(p, 0, 1), then μ = x − zσ.
Why use z (μ=0, σ=1) when σ is unknown?
invNorm needs σ to return x directly; with σ unknown you must work through the standardised z.
If P(X < a) = 0.1, what is the sign of z?
Negative — a left-tail probability below 0.5 gives a negative z.
Topic 4.12 study notes
Full notes & explanations for z-values & inverse normal
Math AA SL exam skills
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