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Grey Kangaroos Are Large, Social Marsupials, Indigenous to Australia

question 4

Essay

Grey Kangaroos are large, social marsupials, indigenous to Australia. As part of a study of the development of these creatures, biologists have measured various aspects of their skeletal structure. A sample of 148 palate widths was taken from skeletal remains and the data is presented in the stem-and-leaf plot below. The distributions of skeletal measures are generally thought to be approximately normal, which is consistent with the stem-and-leaf plot for this sample. The display uses five lines for each stem. Thus, "2t|" is the stem for palate widths of 22 and 23, "2f|" for 24 and 25, "2s|" for 26 and 27, and so on. (The "t" then stands for leaves that are twos and threes, the "f" for leaves of fours and fives, etc.) The mean palate width of this sample is 2.6 cm, and the standard deviation is 0.3 cm.
(a)If this sample is a good representation of the population of Grey Kangaroos, approximately what percent of palate widths in this sample would exceed 2.9 cm?
(b)What is the approximate percentile of a palate width that is 2.0 cm?
(c)One measure of variability is the length of an interval that contains the middle 90% of the values of a distribution. For these data, how long is that interval?

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