1) Fred was told by his teacher that the mean final mark of all the students in his class was exactly 68.7. He surveyed these students and recorded the results in a frequency table with intervals 1-10, 11-20, etc. Will his calculated mean equal the one calculated by his teacher? Explain why or why not.
2) Explain what information is given by the magnitude and sign of the z-score of a piece of data.
3) When is the standard deviation larger than the variance? Explain with an example.
4) The lengths, in centimetres, of wooden pencils are normally distributed with a mean of 15 and a standard deviation of 0.1. Find two intervals of pencil lengths that will each include 81.5% of pencils.