The height of a species of monkey has a normal distribution with mean $56.2$ cm and standard devia

Question

The height of a species of monkey has a normal distribution with mean $56.2$ cm and standard deviation of $\sqrt{15}$ cm. A random sample of $20$ monkeys is taken and the mean height is calculated. Find the probability that The sample mean lies between $55$ cm and $57$ cm, $P\left( X_{1}+X_{2}+\dots+X_{20}>11\mathrm{ m} \right)$

Accepted Answer

(i) $0.739$ (ii) $0.917$

Sample Mean

Sample Mean

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