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3 problems match “rounding”. Clear

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1. Fire extinguishers for a building ●○○○○ 10 ptsOne fire extinguisher is recommended for every 6,000 square feet of a building. How many fire extinguishers are needed for a building of 135,000 square feet? Give the smallest whole number of extinguishers that provides at least one per 6,000 square feet.
2. Smallest maximum rounding error ●●○○○ 20 ptsThe sum of the following seven numbers is exactly 19: $a_1 = 2.56,$ $a_2 = 2.61,$ $a_3 = 2.65,$ $a_4 = 2.71,$ $a_5 = 2.79,$ $a_6 = 2.82,$ $a_7 = 2.86.$ Each $a_i$ is approximated by an integer $A_i,$ for $1 \le i \le 7,$ such that the sum of the $A_i$'s is also $19.$ Let $M$ be the maximum of the seven errors $|A_i - a_i|.$ What is the smallest possible value of $M$? Give your answer as a decimal.
3. Proportion exceeding a rounded threshold ●●●○○ 50 ptsThe tensile strength of a metal component is normally distributed with mean $10000$ kg/cm² and standard deviation $100$ kg/cm². Each measurement is recorded to the nearest $50$ kg/cm². A measurement counts as exceeding $10150$ when its recorded value is greater than $10150$. What proportion of the measurements exceed $10150$ kg/cm²? Round to four decimal places.