The table below shows the percentage points of the normal distribution. The values
in the table are those which a random variable
exceeds with probability
.

| 
| 
| 
|
0.5000 | 0.0000 | 0.0500 | 1.6449 |
0.4000 | 0.2533 | 0.0250 | 1.9600 |
0.3000 | 0.5244 | 0.0100 | 2.3263 |
0.2000 | 0.8416 | 0.0050 | 2.5758 |
0.1500 | 1.0365 | 0.0010 | 3.0902 |
0.1000 | 1.2816 | 0.0005 | 3.2905 |
The Monkey Puzzle Tree Marketing Board has proposed a new scheme that will measure the puzzlingness of monkey puzzle trees in terms of a unit called the ‘fuddle’. It is found that the puzzlingness measurements,
, of monkey puzzle trees grown on the We ♥ Puzzling Monkeys monkey puzzle tree plantation can be modelled as a normal distribution with mean
fuddles and standard deviation
fuddles. Because the owners of the plantation are committed to making sure that the monkey puzzle trees they sell to gardeners are neither too puzzling nor not puzzling enough, the plantation only considers monkey puzzle trees to be saleable if their puzzlingness falls into the 10% to 97.5% interpercentile range of the plantation’s monkey puzzle tree puzzlingness measurements.
Using the percentage points table for the standard normal distribution, or otherwise, find the range of possible puzzlingness measurements for a saleable monkey puzzle tree. Your answer should be given in terms of
and
.