i am doing an assignment with the following questions and I would like to ask for help since i am a bit confused...
A geodesic drone is using LIDAR, a laser system for measuring distances, to measure its altitude with respect to the ground. The laser’s technical specs tell us that its measurements have normally distributed errors (mean µ = 0m, standard deviation σ = 1m).
Q1: When the drone is resting on the ground (zero altitude), what is the probability of getting a negative altitude measurement?
I understand here we are talking about P(X<0) being X "altitude" but how can i calculate it? If i convert it to the standardized normal distribution, than Z=0..?
Q2: At time t, the drone is flying. We measure the altitude three times in a row and get the following results: 61.4m, 60.9m, 61.8m. Build a 95% confidence interval for the drone’s true altitude at time t.
Here, should i use the mean as mean of the 3 results (mean=61.37) and make the CI as (61.37 - 1.96 * 1; 61.37 + 1.96 * 1 ) ?
Q3: Ten seconds later, at t+ 10, we get three more altitude readings: 63.0m, 61.5m, 62.5m. Do the following hypothesis test: – H0: the drone’s altitude has stayed constant. – Ha: the drone has increased its altitude
Here the hypothesis test is H0: altitude = 61.37 H1: altitude > 61.37 Being ̅x = (63.0 + 61.5 + 62.5)/3 and µ = 61.37, right?