Problem 16: What proportion of pregnancies lasts between 240 and 280 days? Round answer to four decimal places.

In understanding pregnancy duration, we typically consider that full-term pregnancies range from 37 to 42 weeks (approximately 259 to 294 days). To analyze the proportion of pregnancies that last between 240 and 280 days, we can apply a standard normal distribution approach. Assuming the average length of pregnancy is approximately 280 days with a standard deviation of 14 days, we find the Z-scores for 240 and 280 days and then look up these values in a standard normal distribution table. This will give us the area under the curve for full-term pregnancies, which can be converted into a proportion. Calculating the Z-scores: Z for 240 days = (240 - 280) / 14 ≈ -2.86 Z for 280 days = (280 - 280) / 14 = 0 Using the Z-table or a calculator: - For Z = -2.86, the area is approximately 0.0021. - For Z = 0, the area is 0.5000. Thus, the proportion of pregnancies lasting between 240 and 280 days is 0.5000 - 0.0021 = 0.4979. After rounding to four decimal places, the answer is 0.4979.