Suppose that a particular bend in an interstate highway is designed for a maximum speed of 78 mph. Data collected previously show that the top speed for automobiles in dry conditions around this bend is normally distributed with a mean of 67 mph and a standard deviation of 3.3 mph. A researcher for the state's transportation department wants to know if the mean top speed of automobiles going around this bend is still 67 mph or if it has changed. He plans to use a one-sample z ‑test for a population means using the established standard deviation of 3.3 mph. He measures the top speeds of six randomly selected automobiles going around this bend in dry conditions. The speeds of these automobiles, in miles per hour, are given below. 69, 67, 70, 75, 73, 45 Is the researcher justified in using a one-sample z‑test for the mean top speed of all automobiles going around this bend? Why or why not?
a) No, because the sample data has a significant outlier.
b) No, because the population standard deviation is not known.
c) Yes, all the requirements are met. The sample is a simple random sample from a normal population with known standard deviation.
d) No, the population is not known to have a normal distribution.
e) No, because the sample is biased.