The height of a species of plant has a normal distribution with mean $34$ cm and standard deviatio

Question

The height of a species of plant has a normal distribution with mean $34$ cm and standard deviation of $\sqrt{78}$ cm. A random sample of $13$ plants is taken and the mean height is calculated. Find the probability that The sample mean lies between $29$ cm and $35$ cm, $P\left( X_{1}+X_{2}+...+X_{13}>450\mathrm{ cm} \right)$

Accepted Answer

(i) $0.638$ (ii) $0.401$

Sample Mean

Sample Mean

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