Question

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

Answer 1

Answer: A. 0.0164

Step-by-step explanation:

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

Standard deviation : $\sigma=15\text{ days}$

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

z-score : $z=\dfrac{X-\mu}{\sigma}$

For X = 300

$z=\dfrac{300-268}{15}\approx2.13$

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

$P(X\geq300)=P(z\geq 2.1333)=1-P(z$

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