Question

1. A chemical process converts lead to gold. However, the production varies due to the powers of the alchemist. It is known that the process is normally distributed, with a standard deviation of 2.5 g. How many samples must be taken to be 90% certain that an estimate of the mean process is within 1.5 g of the true but unknown mean yield? State any assumptions made.

Answer 1

Solution :

Given that,

standard deviation =   =2.5

Margin of error = E = 1.5

At 90% confidence level of z is

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

sample size = n = [Z/2* / E] 2

n = ( 1.645 *2.5 /1.5 )2

n =7.51

Sample size = n =8