Question

The lengths of human pregnancies are normally distributed with a mean of 268 day & a standard deviation of 15 days. What is the probability that a pregnancy last at least 300 days?

Answer 1

The probability that a pregnancy last at least 300 days is 0.01659

Step-by-step explanation:

The formula of z-score is z = (x - μ)/σ, where

• μ is the mean
• σ is the standard deviation
• x is the score

The lengths of human pregnancies are normally distributed with a

mean of 268 day & a standard deviation of 15 days

∴ μ = 268 days

∴ σ = 15 days

We need to find the probability that a pregnancy last at least 300 days

∵ At least means greater than or equal

∴ x ≥ 300 days

For probability that x ≥ 300 find the z-score and use the normal

distribution table to find the area to the right of the z-score

∵ z = (x - μ)/σ

∴ $z=\frac{300-268}{15}$

∴ z = 2.13

By using the normal distribution table of z-score

∵ The area (to the left of z-score) corresponding to z-score of 2.13

   is 0.98341

∵ We need the area to the right of z-score

∴ P(x ≥ 300) = 1 - 0.98341

∴ P(x ≥ 300) = 0.01659

The probability that a pregnancy last at least 300 days is 0.01659

Learn more:

You can learn more about probability in brainly.com/question/9178881

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