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2.4 Probability Distributions

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Question 7

The operational flight time, DDD minutes, of a specialized surveillance drone on a single battery charge is modelled by a normal distribution with mean μ\muμ and standard deviation σ\sigmaσ. Given that μ=45\mu = 45μ=45 and σ=2.5\sigma = 2.5σ=2.5, use standardisation to:

a.

(i) show that P(D<41.5)=0.0808P(D < 41.5) = 0.0808P(D<41.5)=0.0808 to four decimal places. (ii) find the value of d0d_0d0​ such that P(D<d0)=0.0150P(D < d_0) = 0.0150P(D<d0​)=0.0150

[5]
b.

A fleet manager randomly selects 5 drones from the production line.

Calculate the probability that every one of the 5 drones has a flight time exceeding 41.5 minutes.

[2]
c.

A software update is applied to the drones such that the flight time, DDD minutes, now has a mean μ=48\mu = 48μ=48 and a new standard deviation σ\sigmaσ.

Given that P(D<d)=0.0548P(D < d) = 0.0548P(D<d)=0.0548 and P(D>1.5d−21)=0.0082P(D > 1.5d - 21) = 0.0082P(D>1.5d−21)=0.0082,

determine the value of ddd and the value of σ\sigmaσ.

[5]
Markscheme

2.4 Probability Distributions Questions

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

390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.

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