An agricultural scientist is measuring the heights of a specific variety of wheat plants, H H\,H cm, such that H∼N(μ,σ2)H \sim \operatorname{N}(\mu, \sigma^2)H∼N(μ,σ2).
A random sample of these plants is taken, and a 98% confidence interval for μ \mu\,μ is calculated as (78.14,82.26)(78.14, 82.26)(78.14,82.26).
Find, to 2 decimal places, the standard error of the mean.
Hence, or otherwise, calculate a 95% confidence interval for μ \mu\,μ based on the same sample of wheat plants.
Using five different random samples, five 95% confidence intervals for μ \mu\,μ are to be constructed.
Calculate the probability that at least 4 of these intervals will contain μ\muμ.
