Standard +0.3 This is a straightforward application of the Central Limit Theorem to find a probability for a sample mean. Students need to recognize CLT applies (n=50 is large), calculate the mean and variance of the discrete uniform distribution U(11), apply the sampling distribution formula for the mean, and perform a standard normal calculation. While it requires multiple steps, each is routine and the question explicitly tells students to use an approximate method, making it slightly easier than average.
3. A discrete random variable \(X\) has the distribution \(\mathrm { U } ( 11 )\).
The mean of 50 observations of \(X\) is denoted by \(\bar { X }\).
Use an approximate method (continuity correction is not required), which should be justified, to find \(P ( \bar { X } \leq 6.10 )\). [0pt]
3. A discrete random variable $X$ has the distribution $\mathrm { U } ( 11 )$.
The mean of 50 observations of $X$ is denoted by $\bar { X }$.\\
Use an approximate method (continuity correction is not required), which should be justified, to find $P ( \bar { X } \leq 6.10 )$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q3 [6]}}