Discrete random variables — Question 175
Original QCE Vault practice · 5 marks
Q175 · Practice questionTechnology-activeComplex unfamiliar5 marks
QUESTION 175 (5 marks)
A binomial random variable X has mean 4.8 and variance 2.88. Determine the parameters n and p, and hence calculate P(X≥6). WORKED SOLUTION
Practice marking scheme
5 marksANSWERn=12, p=0.4 and P(X≥6)≈0.3348. Worked solution
For a binomial variable, np=4.8 and np(1−p)=2.88. Dividing gives 1−p=0.6, so p=0.4, then n=12. Evaluate the upper tail for X∼Bin(12,0.4). States the mean equation np=4.8. [1 mark]States the variance equation.
[1 mark]Evaluates the required binomial probability.
[1 mark]Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
View the QCAA syllabusHow many marks did you earn?Compare your working with the guide above.
Related questions
- Q5 · Original practice · 1 mark
A discrete random variable X has P(X=x)=k(x+1) for x=0,1,2. Determine k. Discrete random variables - Q15 · Original practice · 1 mark
For a discrete random variable, P(X=0)=0.2, P(X=1)=0.5 and P(X=2)=0.3. Determine E(X). Discrete random variables - Q25 · Original practice · 1 mark
Let X∼Bin(3,0.4). Determine P(X≥2∣X≥1), to three decimal places. Discrete random variables - Q30 · Original practice · 3 marks
Let X∼Bin(5,0.3). Determine P(X=2) to four decimal places. Discrete random variables