In a school with $1200$ students, an average of $1$ out of $20$ students is sick in a week. St

Question

In a school with $1200$ students, an average of $1$ out of $20$ students is sick in a week. State, in this context, two assumptions needed for the number of students who are sick in a week to be well modelled by a binomial distribution. Explain why one of these assumptions may not be met.[3] For the rest of this question, assume that the number of students who are sick in a week has a binomial distribution. Find the expected number of students who are sick in a week.[1] In a class of $25$ students, find the probability that at least $2$ of them are sick in a week.[2] In a sample of $10$ classes with $25$ students each, find the probability that less than five classes have at least $2$ students who are sick in a week, given that there are at least two such classes.[4] Find the least value of $n$ such that in a sample of $n$ randomly selected students, the probability that at least $6$ are sick in a week is more than $0.95$.[3]

Accepted Answer

(i) constant probability and independence, with independence possibly failing because illness is contagious (ii) $60$ (iii) $0.358$ (iv) $0.712$ (v) $208$

Discrete Random Variables (DRV) - Minimum Number of Binomial Trials

Discrete Random Variables (DRV) - Minimum Number of Binomial Trials

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