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In an examination the number of marks allotted to each candidate is an integer. If the marks were normally distributed, and the distribution had a mean of 45 and a standard deviation of 12, find the percentage of the candidates who would pass with a pass mark of 40

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Hint: $P(X\geq 40)=1-P(X\leq 40)=1-\Phi\left( \frac{40-\mu}{\sigma} \right)=1-\Phi\left( \frac{40-45}{12} \right)$,

where $X \sim \mathcal N(45,12^2)$

$\Phi(z)$ is the cdf of the standard normal distribution. A table for the corresponding probabilities can be found here.

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