Find the indicated percentage for the normally distributed variable. Round your answer to two decimal places, if necessary.
-The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a human pregnancy lasts at least 289 days?

Question

Quizplus · Accepted Answer

To find the probability that a human pregnancy lasts at least 289 days, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest (289 days), μ is the mean (268 days), and σ is the standard deviation (15 days). Calculating the Z-score gives us Z = (289 - 268) / 15 = 21 / 15 = 1.4. Looking up the Z-score of 1.4 in a standard normal distribution table or using a calculator, we find that the area to the left of Z = 1.4 is approximately 0.9192, which means the area to the right (the probability of a pregnancy lasting at least 289 days) is 1 - 0.9192 = 0.0808 or 8.08%.

Find the Indicated Percentage for the Normally Distributed Variable