Question

In preparation for a club social, you brought a large number of chewy cookies whose diameter are approximately uniformly distributed with a mean of 5cm. you were told that a quarter of the cookies have a diameter greater than 5.5. find the proportion of cookies whose diameter are between 5.2 to 5.4.

Answer 1

Let the diameter be represented by D. Then,
D~Uniform(a,b)
Mean of unifor distribution is :

which is given to be 5
So, a+b = 10
Given: Quarter of the cookies i.e. 0.25 have diameter greater than 5.5
So ,

Solving, we get
0.25a + 0.75b = 5.5
=> a+3b = 22
Simultaneously solving :
a + b = 10 and,
a + 3b = 22
we get:
a = 4, b = 6
So diameter D ~ Uniform(4,6)
Proportion of cookies having diameter between 5.2 and 5.4:
P(5.2 < D < 5.4) =
10% of the cookies have diameter between 5.2 and 5.4 cm