(a)[3]
Find $P(\bar{X} > 36)$.
(b)[3]
It is given that $P(\bar{X} < a) = 0.986$. Find $a$.
Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
The population follows a normal distribution with mean $35$ and standard deviation $8.1$. A random sample of size $140$ is selected from this population, and the sample mean is denoted by $\bar{X}$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The standardised value is $\frac{36-35}{8.1\sqrt{140}} = 1.461$.” …
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