SPS SPS FM Statistics 2024 January — Question 1 4 marks

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2024
SessionJanuary
Marks4
TopicLinear combinations of normal random variables
TypeKnown variance confidence interval
DifficultyModerate -0.8 This is a straightforward application of the standard confidence interval formula for a normal distribution with known variance. It requires only direct substitution into the formula CI = x̄ ± z*σ/√n with no conceptual challenges or multi-step reasoning—purely routine calculation that any well-prepared student should execute quickly.
Spec5.05d Confidence intervals: using normal distribution

1. The continuous random variable \(X\) has the distribution \(\mathrm { N } ( \mu , 30 )\). 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.

1.

The continuous random variable $X$ has the distribution $\mathrm { N } ( \mu , 30 )$. 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.\\

\hfill \mbox{\textit{SPS SPS FM Statistics 2024 Q1 [4]}}