Zadanie 5
A process duration H is normally distributed with mean μ seconds and standard deviation σ seconds. It is known that P(H > 48) = 0.35 and P(H > 54 ∣ H > 48) = 0.40. Find μ and σ.
Standardization and unknown normal parameters
Use standardized normal values to obtain probabilities, quantiles or unknown distribution parameters.
Tę umiejętność sprawdza 15 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 15 Otwórz w wyszukiwarce z filtrami
Zadanie 10b
For type S, P(S<200)=0.30854 and P(200<S<224)=0.62465. Find μ and σ.
Zadanie 10a
(i) Find μ,σ. (ii) Find P(15<T<22).
Zadanie 4c
Find s.
Zadanie 10f
At a second factory resistance is normal with unknown mean μ and standard deviation σ. Exactly 84% pass the same inspection thresholds. The fraction below 990 Ω is three times the fraction above 1030 Ω. Find μ.
Zadanie 4a
Given μ+Aσ=45, find A.
Zadanie 4b
Find μ and σ.
Zadanie 3b
The probability that X exceeds its mean by more than k standard deviations is.08. Find k.
Zadanie 4
A calibrated sensor has normally distributed response delay D with mean 18 milliseconds and unknown standard deviation σ. Its interquartile range is 0.42 milliseconds. Find σ.
Zadanie 10b
Find μ and σ.
Zadanie 10d
Find the standard deviation d for the second calibration F.
Zadanie 10b
Find μ and σ.
Zadanie 10d
Find the standard deviation d for the second calibration F.
Zadanie 11d
Line A is adjusted: its mean stays 120 μm but its standard deviation becomes σ>0. Line B and the output proportions are unchanged. The combined probability of thickness below 117 μm is now 0.18. Find σ.
Zadanie 10d
Thresholds a<b satisfy P(a≤T≤b)=0.88 and P(T>b)=2P(T<a). Find the lower threshold a.