Moderate -0.8 This is a straightforward confidence interval calculation for a normal distribution with known variance. It requires only direct application of the standard formula with no conceptual challenges—students simply need to recall the formula, identify n=8, σ²=30, and use the z-value 1.96. The calculation is routine with minimal steps for 4 marks.
The continuous random variable \(X\) has the distribution \(\text{N}(\mu, 30)\). The mean of a random sample of 8 observations of \(X\) is 53.1.
Determine a 95\% confidence interval for \(\mu\). You should give the end points of the interval correct to 4 significant figures. [4]
The continuous random variable $X$ has the distribution $\text{N}(\mu, 30)$. The mean of a random sample of 8 observations of $X$ is 53.1.
Determine a 95\% confidence interval for $\mu$. You should give the end points of the interval correct to 4 significant figures. [4]
\hfill \mbox{\textit{OCR Further Statistics 2020 Q1 [4]}}