Discrete random variables — Question 365
Original QCE Vault practice · 4 marks
Q365 · Practice questionTechnology-freeComplex familiar4 marks
QUESTION 365 (4 marks)
X∼Bin(n,p) has mean 6 and variance 9/2. b)Determine P(X=1) exactly. [1 mark] WORKED SOLUTION
Practice marking scheme
4 marksANSWERa) p=1/4, n=24. b) P(X=1)=6(3/4)23. Worked solution
a) np=6 and np(1−p)=9/2. Divide to obtain 1−p=3/4, so p=1/4 and n=24. b) P(X=1)=(124)(1/4)(3/4)23. Exact answers unless rounding is specified; equivalent forms accepted. Retain unrounded intermediate values.
Uses the mean and variance equations.
[1 mark]Obtains an exact binomial probability.
[1 mark]Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
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