Question

Lengths of pregnancies of humans are normally distributed with a mean of 265 days and a standard deviation of 10 days. Use the Empirical Rule to determine the percentage of women whose pregnancies are between 255 and 275 days.

Answer 1

The percentage of women whose pregnancies are between 255 and 275 days is 68.27%.

Step-by-step explanation:

To determine the percentage of women whose pregnancies are between 255 and 275 days, we can use the Empirical Rule. According to the Empirical Rule, for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.

Given that the mean length of pregnancies is 265 days and the standard deviation is 10 days, we can calculate the z-scores for 255 and 275 days:

Z = (x - mean) / standard deviation

Z for 255 days: (255 - 265) / 10 = -1

Z for 275 days: (275 - 265) / 10 = 1

Since we are interested in the percentage between these two values, we need to calculate the area under the curve between -1 and 1 standard deviations from the mean.

Using a standard normal distribution table, we find the area to be approximately 0.6827. Therefore, the percentage of women whose pregnancies are between 255 and 275 days is 68.27%.