The lifespan of a certain type of industrial LED, measured in hours, is assumed to follow a normal distribution with mean $μ\mu$ and variance $σ2\sigma^2$ . Based on data from a single random sample of these LEDs, a $99%99\%$ confidence interval for $μ\mu$ was calculated to be:

(11484.84, 12515.16)

Using the data from this same sample:

Determine a $95%95\%$ confidence interval for $μ\mu$ .

Eight independent random samples are subsequently collected, and a $95%95\%$ confidence interval for $μ\mu$ is constructed for each of these eight samples.

Calculate the probability that exactly 7 of these 8 intervals will contain the true population mean $μ\mu$ .

(11484.84, 12515.16)

Using the data from this same sample:

Determine a $95%95\%$ confidence interval for $μ\mu$ .

Eight independent random samples are subsequently collected, and a $95%95\%$ confidence interval for $μ\mu$ is constructed for each of these eight samples.

Calculate the probability that exactly 7 of these 8 intervals will contain the true population mean $μ\mu$ .

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