Well, it's not clear if the snowman scales by getting taller but no wider or deeper, or scales in all three linear dimensions, or something more like the BMI scale where weight scales in proportion to the square of linear dimension.
The weight of the snow is proportional to the volume. Let's assume the snowman scales in all three dimensions so we use the third power.
Answer:
And if we solve for a we got
And for this case the answer would be 35185 the lowest 1% for the salary
Step-by-step explanation:
Let X the random variable that represent the salary, and for this case we can assume that the distribution for X is given by:
Where and
And we want to find a value a, such that we satisfy this condition:
(a)
(b)
We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.01 of the area on the left and 0.99 of the area on the right it's z=-2.33. On this case P(Z<-2.33)=0.01 and P(z>-2.33)=0.99
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
And for this case the answer would be 35185 the lowest 1% for the salary