Every student in a large school measures the distance from the front door of the school to the flagpole using a meterstick. The results are normally distributed with mean 12.45 m and standard deviation 0.36 m.
a. Find the z-value that corresponds to a measurement of 12.00 m.
b. What is the probability that a randomly chosen measurement is between 12.30 and 12.60 m?
c. Nine students, who were absent on measurement day, measured the distance the next day. What is the probability that the mean of their measurements is between 12.30 and 12.60 m?
d. Find the 95% confidence interval for a single measure.
e. Find the 95% confidence interval for the mean of nine measurements.