Binomial with derived parameters

Questions where n or p must be derived from given information (e.g., 'average number of 5s was 4.8' to find p, or 'mean number of defectives is 1.6' in packs of 20) before calculating probabilities.

3 questions · Moderate -0.1

2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities
Sort by: Default | Easiest first | Hardest first
CAIE S1 2011 June Q1
4 marks Standard +0.3
1 A biased die was thrown 20 times and the number of 5 s was noted. This experiment was repeated many times and the average number of 5 s was found to be 4.8 . Find the probability that in the next 20 throws the number of 5 s will be less than three.
CAIE S1 2009 November Q1
5 marks Moderate -0.3
1 The mean number of defective batteries in packs of 20 is 1.6 . Use a binomial distribution to calculate the probability that a randomly chosen pack of 20 will have more than 2 defective batteries.
CAIE S1 2002 June Q7
10 marks Moderate -0.3
  1. A garden shop sells polyanthus plants in boxes, each box containing the same number of plants. The number of plants per box which produce yellow flowers has a binomial distribution with mean 11 and variance 4.95.
    1. Find the number of plants per box. [4]
    2. Find the probability that a box contains exactly 12 plants which produce yellow flowers. [2]
  2. Another garden shop sells polyanthus plants in boxes of 100. The shop's advertisement states that the probability of any polyanthus plant producing a pink flower is 0.3. Use a suitable approximation to find the probability that a box contains fewer than 35 plants which produce pink flowers. [4]