The height to which a high jumper can clear is normally distributed with mean 1.80 m1.80\text{ m}1.80 m and standard deviation 0.12 m0.12\text{ m}0.12 m.
Using standardisation, show that the probability that this jumper clears less than 1.74 m1.74\text{ m}1.74 m is 0.30850.30850.3085.
This jumper enters a competition. To qualify for the gala, they have up to 3 attempts to clear a height of more than 1.74 m1.74\text{ m}1.74 m. Once they qualify, they do not take any remaining attempts.
Given that they qualified for the gala and that all jumps are independent,
find the probability that this athlete qualified for the gala on their second jump with a height of more than 1.98 m1.98\text{ m}1.98 m.