The gestation period for human births can be taken as normally distributed with a mean of 266 days and a standard deviation of 16 days. If a gestation period is 276 days, what percentile among human births is this?

74th percentile among human births.

Step-by-step explanation:

Problems of normally distributed samples are 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 this problem, we have that:

If a gestation period is 276 days, what percentile among human births is this?

This is the pvalue of Z when X = 276. So

has a pvalue close to 0.74.

So this is the 74th percentile among human births.

The correct answer is A. The Slope is not negative one but it is positive one which means that choice c is incorrect