Question

A confectionery company normally produces bocks of chocolate that average 250 grams in size. Management have decided to reduce the average block
size down to 200 grams. This requires new moulds and adjustments to the machine that squirts the chocolate into the moulds. The chocolate squirting
machine does not have a dial controlling the amount squirted into each mould. Instead the mechanics need to use a trial and error process of adjusting
the pressure of the chocolate and the timer for the valve. Experience has shown that the standard deviation of the amount of chocolate squirted each time
is 9 grams. How many test blocks of chocolate need to be made after each adjustment if management want to be 90% sure that the mean amount of
chocolate squirted into each block is accurate to within 4 grams.
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Answer 1

Here we want to find sample size( n ).

For testing the mean of the population we use Z critical value.

The formula of sample size is as follows:

Where Z_c is the critical value for confidence level = c = 0.90

= standard deviation = 9

ME = Margin of Error = 4

We want to find Z_c

Let = 1 - c = 1 - 0.90 = 0.10

= 0.10/2 = 0.05

So we need tp find Zc   such that   P( Z > Z_c ) = 0.05.

This implies that P( Z < Z_c ) = 1 - 0.05 = 0.95

Using excel

Z_c = "=NORMSINV(0.95)" = 0.645

Plugging the values of Z_c,  , and ME in the formula of n, we get

So the answer of this question is 14