2.4.4 Mean and variance of the binomial (A-level only)

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]

2.4.4 Mean and variance of the binomial (A-level only) Questions