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Answer:
A gestation length of 279 days represents the 18th percentile.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In a certain breed of cattle, the length of gestation has a mean of 284 days and a standard deviation is 5.5 days.
This means that
What length of gestation, rounded to the nearest whole number, represents the 18th percentile?
This is X when Z has a pvalue of 0.18. So X when Z = -0.915.
A gestation length of 279 days represents the 18th percentile.