1. An aircraft manufacturer studied the distance required for take-off of aircraft which is a normally distributed random variable. A sample of 6 planes tested gave the following data:

Distance required for take-off in metres: 500, 510, 520, 530, 540, 500

Compute the 95 percent confidence interval for the true mean take-off distance.

2. The noise level (in decibels) of a lawnmower engine is known to have a standard deviation of 5 decibels. In a sample of 9 lawnmowers tested the mean was 96 decibels. Construct a 95 percent confidence interval for the true mean noise level.

3. A random sample survey revealed that 55 out of 200 employees of a company took public transit to the office. Calculate the 98 percent confidence limits as to the true proportion of office goers who use public transit.