select the correct answer.\nthe numbers of pages in the books in a library follow a normal distribution. if…
select the correct answer.\nthe numbers of pages in the books in a library follow a normal distribution. if the mean number of pages is 180 and the standard deviation is 30 pages, what can you conclude?\n\na. about 60% of the books have fewer than 150 pages.\nb. about 16% of the books have fewer than 150 pages.\nc. about 95% of the books have more than 150 pages.\nd. about 16% of the books have more than 150 pages.
Answer
Explanation:
Step1: Calculate the z - score
The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 150$, $\mu=180$, and $\sigma = 30$. So $z=\frac{150 - 180}{30}=\frac{- 30}{30}=-1$.
Step2: Use the properties of the normal distribution
In a normal distribution, about 68% of the data lies within 1 standard - deviation of the mean ($\mu\pm\sigma$), which means that the area between $z=-1$ and $z = 1$ is approximately 68%. The total area under the normal curve is 100%. The area to the left of $z=-1$ is $\frac{100 - 68}{2}=16%$. This means that about 16% of the books have fewer than 150 pages.
Answer:
B. About 16% of the books have fewer than 150 pages.