Question

The weight, in kilograms, of cereal in a box can be modelled by a normal distribution with Mean ? and standard deviation 5.4 kg. Given that 10% of boxes contains less than D kg. Find.

a. The value of ?.

b. The percentage of boxes that contain more than (D+4) kg.

c. If the machine settings are adjusted so that the weight of cereal in a box is normally distributed with mean (D+3) kg and standard deviation of ?. Given that the probability of boxes contains between D kg and (D+6) kg is 0.9671, find the value of ?.

note: D=18

Answer 1

Let ,

a. we have ,

.............(I)

From standard normal distribution table , .............(II)

From (I) and (II) , we get ,

b. Now ,

; From standard normal distribution table

c. We have ,

Now ,

............(I)

From standard normal distribution table , .............(II)

From (I) and (II) , we get ,