For a given population of high school seniors, the Scholastic Aptitude Test (SAT) in mathematics has a mean score of 550 with a standard deviation of 100. SAT scores are normally distributed.

What is the probability that a randomly selected high school senior's score on the mathematics part of the SAT will be more than 680? (Please answer in 4 decimal places after decimal point.)

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What is the probability that a randomly selected high school senior's score on the mathematics part of the SAT will be less than 405? (Please answer in 4 decimal places after decimal point.)

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What is the probability that a randomly selected high school senior's score on the mathematics part of the SAT will be between 405 and 680?(Please answer in 4 decimal places after decimal point.)

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Suppose that an engineering school program will accept only high school seniors with mathematics SAT in the bottom 15%. What is the cutoff SAT score in mathematics for this program? (Please answer in a whole number.)

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Suppose that an engineering school program will accept only high school seniors with mathematics SAT in the top 25%. What is the cutoff SAT score in mathematics for this program?(Please answer in a whole number.)

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