The mean gestational length of a sample of 208 horses is 343.7 days, with a standard...
The mean gestational length of a sample of 208 horses is 343.7 days, with a standard deviation of 10.4 days. The data set has a bell-shaped distribution.
a) Estimate the number of gestation lengths between 333.3 and 354.1 days.
b) Determine whether a gestation length of 318.4 days feet is unusual.
Homework Answers
a) The data set has a bell-shaped distribution with mean = 343.7 and standard deviation of 10.4 days.
We need to find:
P(333.3 < X < 354.1) = P((333.3 - 343.7)/10.4 < z < (354.1 - 343.7)/10.4) = P(-1 < z < 1)
= P(z < 1) - P(z < -1)
= 0.8413 - 0.1587
= 0.6826
Hence, the number of gestation lengths between 333.3 and 354.1 days = P x 208 = 0.6826 x 208 = 142 approximately
b) A gestation length would be unusual if it falls outside the two standard deviations of the mean.
Lower bound: 343.7 - 2*10.4 = 322.9
As 318.4 days is less than 322.9 (lower bound), it is unusual.
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