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The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 10 days. Find the probability of a pregnancy lasting 310 days or longer.

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Final answer:

To find the probability of a pregnancy lasting 310 days or longer, we calculate a z-score with the given mean of 268 days and standard deviation of 10 days. With a z-score of 4.2 for 310 days, the probability is extremely low and approaches zero, indicating that such an event is statistically very unlikely.

Step-by-step explanation:

To find the probability of a pregnancy lasting 310 days or longer, we use the normal distribution properties. With a mean (μ) of 268 days and a standard deviation (σ) of 10 days, we must first compute the z-score for 310 days. The z-score formula is Z = (X - μ) / σ, where X is the value for which we're finding the probability.

The z-score for a 310-day pregnancy is calculated as follows: Z = (310 - 268) / 10 = 42 / 10 = 4.2. Once we have the z-score, we consult the standard normal distribution table or use a calculator with normal distribution functions to find the probability corresponding to a z-score of 4.2. However, since 4.2 is significantly beyond the typical z-score values listed on a standard table, the probability of a z-score being 4.2 or above is extremely low, effectively approaching zero.

The probability of a pregnancy lasting 310 days or longer is, therefore, statistically very unlikely.

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