Mean of a normal distribution with known standard deviation from one cumulative probability, then the probability of exceeding a length

The lengths of cucumbers grown on a farm are normally distributed with standard deviation \(2.4\text{ cm}\). The probability that a randomly chosen cucumber is shorter than \(31\text{ cm}\) is \(0.83\).

1. Find the mean length of the cucumbers.
2. Find the probability that a randomly chosen cucumber is longer than \(27\text{ cm}\).

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