Expert: Ahmed Salami - 10/29/2008

Question
Soup is sold in tins which are filled by a machine.  The actual weight of soup delivered to a tin by the filling machine is always normally distributed about the mean weight with a standard deviation of 8g.  The machine is set originally to deliver a mean weight of 810g.

(a) Determine the probability that the weight of soup in a tin, selected at random, is less than 800g.

(b) Determine the probability that the weight of soup in a tin, selected at random, is between 795 g and 820 g.


Please do not mind the questions i ask, its just that i am finding this topic very difficult, all help is much appricieated. Thank you again

Answer
Hi Syed,
Its okay, you can always ask your questions.
The z statistic for any weight w is
z = (w - m)/s
where m is the mean and s is the standard deviation
m = 810g and s = 8g
a)For the weight 800g,
z = (800 - 810)/8
 = -10/8
 = -1.25

We need to find the area(i.e probability) to the left of z = -1.25
From tables,
p = 0.1056

b)For the weight 795g
z = (795 - 810)/8
 = -15/8
 = -1.875
For the weight 820g,
z = (820 - 810)/8
 = 10/8
 = 1.25
The probability of a weight to be between 795g and 820g is the
area between z = -1.875 and z = 1.25, which from tables is
0.4696 + 0.3944 = 0.864

Note that usual statistical tables gives you the area between 0 and z.
Let me know if you have any kind of problem with using the
table.

Regards.