Question

The average thickness of books on a library shelf is 8.3 centimeters. The standard deviation is 0.6 centimeter. If 20% of the books are oversized, find the minimum thickness of the oversized books on the library shelf. Assume the variable is normally distributed.

Answer 1

Answer:

8.8 cm

Step-by-step explanation:

-We know that the top 20% of the books are oversized.

-We therefore find the z-value of the top 20%:

$z_{0.1}=8.4$

#We substitute the z value in formula to solve X.

$z=\frac{\bar X-\mu}{\sigma}$

Where

• X is the minimum thickness of the book.

-Given $\sigma=0.6 \ , \mu=8.3$, the minimum thickness,X can be calculated as follows:

$z=\frac{\bar X-\mu}{\sigma}\\\\0.84=\frac{\bar X-8.3}{0.6}\\\\\bar X=0.84\times 0.6+8.3\\\\=8.804\approx 8.8\ cm$

Hence, the minimum thickness of the oversized books is 8.8 cm