Assignment I for Biostats Course VHM 801 at AVC - Fall semester 2001

The data below are percentages of butterfat from 120 registered three-year-old Ayrshine cows selected at random from a Canadian stock record book.

1. Carry out a descriptive analysis of the data, with particular emphasis on the center, spread and shape of the distribution, as well any potentially outlying observations.
2. Examine whether it would seem reasonable to assume the data to be normally distributed, or whether a normal distribution would fit better to the transformed data (log or square-root transformation).
3. Based on the data, the task is to calculate approximately the probability that the percentage of butterfat in a three-year-old Ayrshine cow exceeds 4.50.
   • First, without assuming a particular distribution for butterfat percentages.
   • Second, assuming a normal distribution for butterfat percentages (or the log-transformed butterfat percentages, if your analysis show them to better approximated by a normal distribution). Hint: Use the mean and standard deviation calculated from the data as parameters in the normal distribution.

Data:

4.32 4.24 4.29 4.00 3.96 4.48 3.89 4.02 3.74 4.42
4.20 3.87 4.10 4.00 4.33 3.81 4.33 4.16 3.88 4.81
4.23 4.67 3.74 4.25 4.28 4.03 4.42 4.09 4.15 4.29
4.27 4.38 4.49 4.05 3.97 4.32 4.67 4.11 4.24 5.00
4.60 4.38 3.72 3.99 4.00 4.46 4.82 3.91 4.71 3.96
3.66 4.10 4.38 4.16 3.77 4.40 4.06 4.08 3.66 4.70
3.97 3.97 4.20 4.41 4.31 3.70 3.83 4.24 4.30 4.17
3.97 4.20 4.51 3.86 4.36 4.18 4.24 4.05 4.05 3.56
3.94 3.89 4.58 3.99 4.17 3.82 3.70 4.33 4.06 3.89
4.07 3.58 3.93 4.20 3.89 4.60 4.38 4.14 4.66 3.97
4.22 3.47 3.92 4.91 3.95 4.38 4.12 4.52 4.35 3.91
4.10 4.09 4.09 4.34 4.09 4.88 4.28 3.98 3.86 4.58