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ANSWER:
Almost all (99.7%) horse pregnancies fall in what range of lengths?
Good job! The Standard Deviation Rule tells us that virtually all the data fall within 3 standard deviations of the mean, which in this case is exactly between 336 - 3(3) = 327, and 336 + 3(3) = 345.
What percentage of horse pregnancies last longer than 339 days?
16%
Good job! According to the SD rule, 68% of horse pregnancies last between 336 - 3 = 333 and 336 + 3 = 339 days, which means that the remaining 32% of horse pregnancies are divided evenly between lasting less than 333 days and lasting more than 339 days. We, therefore, conclude that 16% of horse pregnancies last more than 339 days.
The body temperatures of dogs are normally distributed with a mean of 101.3°F and a standard deviation of .6°F. Use this information to answer the following questions:
About 95% of the temperatures of dogs fall within which range?
100.1-102.5
Good job! The Standard Deviation Rule tells us that 95% of the temperatures fall within 2 SD of the mean. In this case, this is between 101.3 - 2(.6) = 100.1 and 101.3 + 2(.6) = 102.5.
Another example:
In general, the larger the animal the longer the length of pregnancy (also called gestation period). For the horse, for example, the gestation period varies roughly according to a normal distribution with a mean of 336 days and a standard deviation of 3 days. (Source: These figures are from Moore and McCabe, Introduction to the Practice of Statistics.) Use the Standard Deviation Rule to answer the following questions: (a picture of the SD rule applied to this distribution will help).