The normal distribution and when to use it Problem set B Answers

1. (a) Mean 7, standard deviation 1.87
2. (b) Symmetric and bell-shaped, centred on the mean

1. (a) 95%
2. (b) 16%
3. (c) 47.5%

No. The box plot is skewed to the right.

Yes, it is reasonable: the data is roughly symmetric.

1. (a) 1.45
2. (b) The mean is less than 2 standard deviations from the limit, so a normal model gives a noticeable probability to values that cannot happen.

1. (a) 78.8 to 81.2 mm
2. (b) 3.75 standard deviations above the mean; it is unusual.

1. (a) Mean 1.8, standard deviation 1.24
2. (b) 1.46
3. (c) The mean is less than 2 standard deviations from 0, so the pile is bunched against the left wall and skewed to the right.