Xiang is designing shelves for a bookshop. The height, \(H \mathrm {~cm}\), of books is modelled by the normal distribution with mean 25.1 cm and standard deviation 5.5 cm
Show that \(\mathrm { P } ( H > 30.8 ) = 0.15\)
Xiang decided that the smallest \(5 \%\) of books and books taller than 30.8 cm would not be placed on the shelves. All the other books will be placed on the shelves.
Find the range of heights of books that will be placed on the shelves.
(3)
The books that will be placed on the shelves have heights classified as small, medium or large.
The numbers of small, medium and large books are in the ratios \(2 : 3 : 3\)
The medium books have heights \(x \mathrm {~cm}\) where \(m < x < d\)
Show that \(d = 25.8\) to 1 decimal place.
Find the value of \(m\)
Xiang wants 2 shelves for small books, 3 shelves for medium books and 3 shelves for large books.
These shelves will be placed one above another and made of wood that is 1 cm thick.