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2.4 Statistical Distributions

2.4 Statistical Distributions

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Question 24

A viticulturist is investigating the survival of a new hybrid vine graft. The probability that a graft is successful is denoted by ppp. A sample of 100 grafts is taken, and the random variable S S\,S represents the number of successful grafts, where S∼B(100,p)S \sim \text{B}(100, p)S∼B(100,p).

Using a normal approximation, the probability that S S\,S is at least 53 is 0.0054 to 4 decimal places.

i.

Show that p p\,p satisfies 426.01p2−446.01p+110.25=0426.01p^2 - 446.01p + 110.25 = 0426.01p2−446.01p+110.25=0 when normal probability tables are used.

[6]
ii.

Hence find the value of ppp, justifying your answer.

[2]
Markscheme

2.4 Statistical Distributions Questions

  1. A Level
  2. /Maths
  3. /2.4 Statistical Distributions

390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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