The time taken for James to commute to work, in minutes, is normally distributed with a mean of 35 minutes and a standard deviation of 4 minutes. On a particular morning, James starts his commute.
Find the probability that the commute takes longer than 32 minutes.
James has already been commuting for 32 minutes. Find the probability that his commute lasts for another 8 minutes.
James believes that the mean commute time is longer than 35 minutes. He records a random sample of 16 commutes and finds that their mean time is 36.8 minutes. Stating your hypotheses clearly and using a 5% level of significance, test James' belief.
