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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 pregnancy last at least 300​ days? Round to four decimal places. A. 0.0164 B. 0.9834 C. 0.4834 D. 0.0179

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JeanaShupp

Answer: A. 0.0164

Step-by-step explanation:

Given : The lengths of human pregnancies are normally distributed with a mean [tex]\mu=268\text{ days}[/tex]

Standard deviation : [tex]\sigma=15\text{ days}[/tex]

Let X be the random variable that represents the length of pregnancy of a randomly selected human .

z-score : [tex]z=\dfrac{X-\mu}{\sigma}[/tex]

For X = 300

[tex]z=\dfrac{300-268}{15}\approx2.13[/tex]

Now, the probability that a pregnancy last at least 300​ days will be :-

[tex]P(X\geq300)=P(z\geq 2.1333)=1-P(z<2.1333)\\\\=1- 0.9835513=0.0164487\approx0.0164[/tex]

Hence, the probability that a pregnancy last at least 300​ days =0.0164

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