Question

the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days what is the probability of randomly selecting a pregnant woman whose length of pregnancy is less than 260 days


a.0.2981


b.0.7019


c.0.8186


d.0.1814

Answer 1

Answer:

a. 0.2981

Step-by-step explanation:

We are told that the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

Let us find z-score for 260 days.

$z=\frac{x-\mu}{\sigma}$, where,

$x$ = Sample score,

$\mu$ = Mean  

$\sigma$ = Standard deviation.

Upon substituting our given values in z-score formula we will get,

$z=\frac{260-268}{15}$    

$z=\frac{-8}{15}$  

$z=-0.53$  

Now we will use normal distribution table to find the area that corresponds to z-score of -0.53.  

From normal distribution table we get 0.29806 as our answer. Upon rounding our answer to four decimal places we will get 0.2981 as our answer.

Therefore, probability of selecting the woman whose length of pregnancy is less than 260 days will be 0.2981 and option a is the correct choice.