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2.4.13 Model with probability distributions

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Question 7

The operational lifespans of deep-sea sensor modules, $T$ hours, are normally distributed such that $\sim \text{N}(\mu, 40^2)$ .

Given that $15%15\%$ of the modules have a lifespan exceeding $1200$ hours, calculate the value of $μ\mu$ correct to the nearest $0.1$ h.

[3]

An oceanographer selects $12$ modules at random.

Determine the probability that fewer than $2$ of these modules have a lifespan exceeding $1200$ hours.

[3]

A research station deploys $250$ modules.

By employing a suitable approximation, find the probability that more than $45$ of these modules have a lifespan exceeding $1200$ hours.

[5]

Markscheme

2.4.13 Model with probability distributions Questions

A Level
Maths
2.4.13 Model with probability distributions

67 exam-style questions on OCR (MEI) A Level Maths 2.4.13 Model with probability distributions. Each one has a worked solution and a mark scheme showing where the marks go.

2.4.13 Model with probability distributions

Question bank

2.4.13 Model with probability distributions

Medium Hard

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Question 7

The operational lifespans of deep-sea sensor modules, $T$ hours, are normally distributed such that $\sim \text{N}(\mu, 40^2)$ .

Given that $15%15\%$ of the modules have a lifespan exceeding $1200$ hours, calculate the value of $μ\mu$ correct to the nearest $0.1$ h.

[3]

An oceanographer selects $12$ modules at random.

Determine the probability that fewer than $2$ of these modules have a lifespan exceeding $1200$ hours.

[3]

A research station deploys $250$ modules.

By employing a suitable approximation, find the probability that more than $45$ of these modules have a lifespan exceeding $1200$ hours.

[5]

Markscheme

2.4.13 Model with probability distributions Questions

A Level
Maths
2.4.13 Model with probability distributions

67 exam-style questions on OCR (MEI) A Level Maths 2.4.13 Model with probability distributions. Each one has a worked solution and a mark scheme showing where the marks go.