He is considering taking the first 50 customers who go to the information desk. Explain why this method is unsuitable.
The actual times, in minutes, that customers spend at the information desk may be assumed to have mean $\mu$ and variance $4.8$. The researcher knows that in the past $\mu$ was $6.0$. He wants to test, at the $2\%$ significance level, whether that is still the case. He takes a random sample of 50 customers and records the time each spends at the information desk. State the probability of making a Type I error and explain what is meant by a Type I error in this context.
Given that the mean time spent at the information desk by the 50 customers is $6.8$ minutes, carry out the test.
Give a reason why the Central Limit Theorem had to be used in your answer to part (c).