The height of a lighthouse on the shore may be determined by measuring the horizontal distance L from the center of the lighthouse base to the instrument, and the vertical angle , as shown in the figure below.

(a) The distance L was measured 12 times with the following readings (ft) { 376.6, 376.1, 378.1, 382.8, 381.2, 381.9, 376.9, 379.1, 377.1, 381.8, 374.9, 378.9}. Determine (i) the estimated distance and its standard error; (ii) a 90% confidence interval for estimated distance; (iii) the estimated height and its standard error if the angle = 4025.0', and (iv) a 90% confidence interval for the estimated height if the angle = 4025.0'

(b) The angle was measured 9 times {4025.5, 4010.6', 4030.6', 40 12.3', 4040.6', 4040.9', 40 17.8, 40 21.9', 4018.1'} Determine (i) the estimated angle and its standard error; (ii) a 90% confidence interval for estimated angle; (iii) the estimated height and its standard error if the distance L = 381.0 ft, and (iv) a 90% confidence interval for the estimated height if the distance L = 381.0 ft.

(c) For each of the 12 values for L and each of the 9 values for compute the tower height; now, you have 108 values for the height; using these values, construct a 90% confidence interval for the estimated height.

L 0