The operating life, $L$ hours, of a specialized 'X-7' industrial diode is modeled by a normal distribution with mean $μ\mu$ and standard deviation $σ\sigma$ .

Quality control testing reveals that $10%10\%$ of the diodes fail before reaching $800$ hours of operation, while $20%20\%$ of the diodes exceed a lifespan of $1200$ hours.

Determine the value of $μ\mu$ and the value of $σ\sigma$ .

(i) State the value of $\neq 1000)$ . (ii) Find $P (L < 1000)$ .

These diodes are sold in batches of $12$ . Calculate the probability that, in a randomly selected batch, no more than $3$ diodes have an operating life of less than $1000$ hours. You may assume that the lifespans of the diodes are independent.

The operating life, $L$ hours, of a specialized 'X-7' industrial diode is modeled by a normal distribution with mean $μ\mu$ and standard deviation $σ\sigma$ .

Quality control testing reveals that $10%10\%$ of the diodes fail before reaching $800$ hours of operation, while $20%20\%$ of the diodes exceed a lifespan of $1200$ hours.

Determine the value of $μ\mu$ and the value of $σ\sigma$ .

(i) State the value of $\neq 1000)$ . (ii) Find $P (L < 1000)$ .

4.5.1 Statistical distributions (A-level only)

Question 29

Markscheme

4.5.1 Statistical distributions (A-level only)

Question 29

Markscheme

4.5.1 Statistical distributions (A-level only)

Question 29

4.5.1 Statistical distributions (A-level only) Questions

4.5.1 Statistical distributions (A-level only)

Question 29

4.5.1 Statistical distributions (A-level only) Questions