On average, $40\%$ of Christmas tree light bulbs manufactured by a company are red and the rest ar

Question

On average, $40\%$ of Christmas tree light bulbs manufactured by a company are red and the rest are blue. The lights are sold in boxes of $20$. Assume that the number of red light bulbs in a box has a binomial distribution. Find the probability that a box of $20$ light bulbs contains fewer red light bulbs than blue light bulbs.[1] In $n$ randomly chosen boxes, the probability that there will be at least $2$ boxes with fewer red light bulbs than blue is at most $0.999$. Find the greatest value of $n$.[3] A random sample of $50$ boxes is chosen. Using an approximate distribution, find the probability that the mean number of red light bulbs in $1$ box will not exceed $7.5$.[3] A customer selects boxes of light bulbs at random from a large consignment until she finds a box with fewer red lights than blue. Give a reason why a binomial distribution is not an appropriate model for the number of boxes selected.[1]

Accepted Answer

(i) ${0.755}$ (ii) ${7}$ (iii) ${0.0533}$ (iv) In the context of the question, the number of boxes that the customer can select is not fixed (sample size is not fixed). Hence a binomial distribution is not an appropriate model as it requires a fixed number of trials.

2018 ACJC P2 Q6

2018 ACJC P2 Q6

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