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PENANG FREE SCHOOL MATHEMATICS ELECTIVES- ADDITIONAL MATHEMATICS DAVID CHNG YEANG SOON. Try the following Questions. The answers are provided at the end of the questions. Topic 8 Hard. Name: ……………………………………….. Class:………………….. 1. The height of students in a college has a normal distribution with a mean of 179 cm and a standard deviation of 13.33 cm. Find (a) the height of students in the college which gives a standard score of 0.45, (b) the percentage of students in the college with height greater than 167 cm. [10 marks] 2. The masses of a sample of 110 guava are normal distributed with a mean of 186 g and a standard deviation of 15.909 g. (a) Determine the probability that a randomly selected guava has a mass greater than 193 g. (b) A whole seller wishes to purchase 200 guava, each having a mass greater than 196.977 g. Find the number of guava that must be collected in order to achieve the requirement of the whole seller. [10 marks] 3. The height of students in a college has a normal distribution with a mean of 168 cm and a standard deviation of 18.57 cm. Find (a) the height of students in the college which gives a standard score of 0.47, (b) the percentage of students in the college with height greater than 155 cm. [10 marks] 4. A hot drink machine is regulated so that it dispenses an average of 340 ml of hot drink per cup. Assuming that the volume of hot drink in cup is normally distributed with a standard deviation of 12.273 ml, (a) what is the probability that a cup will contain more than 363 ml? (b) what is the probability that a cup contains between 317 ml and 354.11 [10 marks] ml? 5. The masses of a sample of 120 guava are normal distributed with a mean of 184 g and a standard deviation of 16.204 g. (a) Determine the probability that a randomly selected guava has a mass greater than 191 g. (b) A whole seller wishes to purchase 90 guava, each having a mass greater than 195.019 g. Find the number of guava that must be collected in order to achieve the requirement of the whole seller. [10 marks] 6. The masses of a sample of 80 guava are normal distributed with a mean of 178 g and a standard deviation of 16.204 g. (a) Determine the probability that a randomly selected guava has a mass greater than 185 g. (b) A whole seller wishes to purchase 30 guava, each having a mass greater than 189.051 g. Find the number of guava that must be collected in order to achieve the requirement of the whole seller. [10 marks] 7. The height of students in a college has a normal distribution with a mean of 179 cm and a standard deviation of 36 cm. Find (a) the height of students in the college which gives a standard score of 0.45, (b) the percentage of students in the college with height greater than 161 cm. [10 marks] 8. The masses of a sample of 100 guava are normal distributed with a mean of 187 g and a standard deviation of 16.018 g. (a) Determine the probability that a randomly selected guava has a mass greater than 194 g. (b) A whole seller wishes to purchase 180 guava, each having a mass greater than 197.973 g. Find the number of guava that must be collected in order to achieve the requirement of the whole seller. [10 marks] 9. A hot drink machine is regulated so that it dispenses an average of 350 ml of hot drink per cup. Assuming that the volume of hot drink in cup is normally distributed with a standard deviation of 5.864 ml, (a) what is the probability that a cup will contain more than 361 ml? (b) what is the probability that a cup contains between 339 ml and 356.63 [10 marks] ml? 10. A hot drink machine is regulated so that it dispenses an average of 320 ml of hot drink per cup. Assuming that the volume of hot drink in cup is normally distributed with a standard deviation of 8.021 ml, (a) what is the probability that a cup will contain more than 335 ml? (b) what is the probability that a cup contains between 305 ml and 328.82 [10 marks] ml? 11. A hot drink machine is regulated so that it dispenses an average of 340 ml of hot drink per cup. Assuming that the volume of hot drink in cup is normally distributed with a standard deviation of 13.326 ml, (a) what is the probability that a cup will contain more than 365 ml? (b) what is the probability that a cup contains between 315 ml and 355.19 [10 marks] ml? 12. A hot drink machine is regulated so that it dispenses an average of 290 ml of hot drink per cup. Assuming that the volume of hot drink in cup is normally distributed with a standard deviation of 8.538 ml, (a) what is the probability that a cup will contain more than 306 ml? (b) what is the probability that a cup contains between 274 ml and 299.56 [10 marks] ml? 13. The height of students in a college has a normal distribution with a mean of 166 cm and a standard deviation of 18.75 cm. Find (a) the height of students in the college which gives a standard score of 0.47, (b) the percentage of students in the college with height greater than 151 cm. [10 marks] 14. The masses of a sample of 120 guava are normal distributed with a mean of 162 g and a standard deviation of 11.468 g. (a) Determine the probability that a randomly selected guava has a mass greater than 167 g. (b) A whole seller wishes to purchase 170 guava, each having a mass greater than 169.844 g. Find the number of guava that must be collected in order to achieve the requirement of the whole seller. [10 marks] 15. The height of students in a college has a normal distribution with a mean of 166 cm and a standard deviation of 8.33 cm. Find (a) the height of students in the college which gives a standard score of 0.44, (b) the percentage of students in the college with height greater than 161 cm. [10 marks] Answers: 1. (a) 185 cm (b) 81.6% 2. (a) 0.33 (b) Number of guava = 816 3. (a) 176.73 cm (b) 75.8% 4. (a) 0.0305 (b) 0.8445 5. (a) 0.3329 (b) Number of guava = 363 6. (a) 0.3329 (b) Number of guava = 121 7. (a) 195.2 cm (b) 69.1% 8. (a) 0.3311 (b) Number of guava = 730 9. (a) 0.0303 (b) 0.8404 10. (a) 0.0307 (b) 0.8336 11. (a) 0.0303 (b) 0.8425 12. (a) 0.0305 (b) 0.8382 13. (a) 174.81 cm (b) 78.8% 14. (a) 0.3314 (b) Number of guava = 688 15. (a) 169.67 cm (b) 72.6%