Gce Model Questions Vol1 2017 Mathematics Question 32

Practice objective / multiple choice question 32 from the 2017 Gce Model Questions Vol1 Mathematics examination.

Gce Model Questions Vol1 2017 Mathematics Objective / Multiple Choice Hard Difficulty
Question 32 GCE_MODEL_QUESTIONS_VOL1 • 2017 • MATHEMATICS • objective

In a school, the numbers of subject passes recorded for each student are independent and follow Poisson distributions with means \(4,6,5,3\) and \(7\) for five different subjects. Hence the total number of passes for a randomly chosen student follows a Poisson distribution with mean \(\lambda = 25\). Using a normal approximation with continuity correction, find the probability that a student has at least \(30\) passes, and then the conditional probability that the student has at least \(30\) passes given that they have at least \(20\) passes. Give your answers to three decimal places.

Answer Options

A. P(X≥30)≈0.162 and P(X≥30 | X≥20)≈0.198 (both to three decimal places)
B. P(X≥30)≈0.210 and P(X≥30 | X≥20)≈0.250 (both to three decimal places)
Correct Answer C. P(X≥30)≈0.184 and P(X≥30 | X≥20)≈0.213 (both to three decimal places)
D. P(X≥30)≈0.140 and P(X≥30 | X≥20)≈0.180 (both to three decimal places)
Correct Answer
C
Correct Option:
P(X≥30)≈0.184 and P(X≥30 | X≥20)≈0.213 (both to three decimal places)

About This Question

This is Gce Model Questions Vol1 2017 Mathematics Question 32. It is one of the objective questions from the 2017 Gce Model Questions Vol1 Mathematics examination.

Difficulty level: Hard .

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