Zadanie 10a
For a randomly selected type-R battery find the probability that its duration is (i) below 224 minutes; (ii) between 224 and 242 minutes; (iii) between 224 and 242 minutes given it exceeds 224 minutes.
Normal probabilities with known parameters
Interpret a normal model and use technology to calculate probabilities or quantiles when its mean and spread are given.
Tę umiejętność sprawdza 25 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 25 Otwórz w wyszukiwarce z filtrami
Zadanie 10a
(i) Find μ,σ. (ii) Find P(15<T<22).
Zadanie 5a
Find b such that P(X > b) = P(Y > 34).
Zadanie 5b
Give P(12 − a < X < 12 + a) approximately, to two significant figures.
Zadanie 5c
If a = 4, estimate P(Y < 34) to two significant figures.
Zadanie 10a
Find P(R < 990).
Zadanie 10b
The highest 15% of resistances exceed r ohms. Find r to four significant figures.
Zadanie 10c
What percentage of resistors pass inspection?
Zadanie 5b
Using the normal model with these estimated parameters, find the interquartile range to two significant figures.
Zadanie 2g
Now use the continuous model q(x) = x2 + 2Zx + 4, where Z is normal with mean 0.5 and standard deviation 1.5. Find the probability of two distinct x-intercepts.
Zadanie 2h
In the continuous model q(x) = x2 + 2Zx + 4, with Z normal of mean 0.5 and standard deviation 1.5, suppose the graph has two distinct x-intercepts and . Find the conditional probability that both intercepts are greater…
Zadanie 3a
Find the probability that X is more than 1.2 standard deviations above its mean.
Zadanie 6a
Estimate the percentage of type A pellets with mass greater than 16 g.
Zadanie 6b
A randomly selected pellet has mass greater than 16 g. Estimate the probability that it is type A. Give your answer as a fraction.
Zadanie 3a
Find P(W > 320).
Zadanie 3b
Find P(W < w).
Zadanie 3c
Find w.
Zadanie 10a
Find P(42.2<H<47.8).
Zadanie 10a
Find P(42.2<H<47.8).
Zadanie 8
A sensor of type A gives normally distributed signal readings with mean 48 and standard deviation 4. A type-B sensor has mean 50 and standard deviation 3. Every reading is independent, including across the two sensors. Each sensor is tested four times and…
Zadanie 11a
Find the probability that a line-A piece has thickness below 117 μm.
Zadanie 11c
A piece is selected from the combined output. (i) Find the probability its thickness is below 117 μm. (ii) Given that its thickness is below 117 μm, find the probability it came from line A.
Zadanie 10a
Find P(T>48).
Zadanie 10c
A large collection contains only cycles longer than 48 minutes. (i) Find the probability that a randomly chosen cycle from this collection lasts less than 62 minutes. (ii) Twelve cycles are independently selected from the collection. Find the probability that…
Zadanie 10d
Thresholds a<b satisfy P(a≤T≤b)=0.88 and P(T>b)=2P(T<a). Find the lower threshold a.