1. Solve the following system of equation by Cramer’s
rule.
x1 + x2 + x3 = 10
5x1 - 2x2 + x3 = 3
3x1 + x2 - 4x3 = -1
2. Before constructing a dam on a Hill river, the Army corps of engineers performed a series of tests to measure the water flow past the proposed location of the dam. The results of the testing were used to construct the following frequency distribution:
| River flow (000’s of units per min) | Frequency |
| 1001-1050 | 7 |
| 1051-1100 | 21 |
| 1101-1150 | 32 |
| 1151-1200 | 49 |
| 1201-1250 | 58 |
| 1251-1300 | 41 |
| 1301-1350 | 27 |
| 1351-1400 | 11 |
Use the data given in the table to construct a “more than type” cumulative frequency distribution and ogive.
3. In a large locality, 60% of families have a car, 50% have
an air conditioner and 30% have both. Find the percentage of
families that have
a. At least one of the items
b. Neither of the two
c. Have only air conditioner
4. A central university has a student population of 60,000. The university is interested in determining what proportion of them is in favour of a new grading system. Determine a sample size with confidence level of 95% that will show the true proportion of population in favour of the new system within plus and minus 0.02.
5. A telescope manufacturer wants its telescopes to have standard
deviations in resolution to be significantly below 2 when focusing
on objects 500 light-years away. When a telescope is used to
focus on an object 500 light years away 30 times, the sample
standard deviation turns out to be 1.46.
a. State explicit null and alternate hypotheses
b. Test your hypothesis at the a=0.01 level.