Suppose that students' commuting time at CSN, represented by the variable X, has mean= 29 minutes and standard deviation = 9 minutes. There are 6000 students at CSN and we are about to take a random sample of 40 students.
a) Can we know in advance what the mean commuting time for the students in the sample will be?
b) Calculate the probability that the sample mean will be within 2 minutes of the population mean.
c) If we increase sample size from 40 to 100, what will happen to the probability of observing the sample mean within 2 minutes from the population mean?
Step-by-step solutions for all the three parts using standard normal distribution.