Question

Q. A scientist plans to perform a series of measurements to find the diameter of a particle in nanometer (nm). He believes that the values obtained from the measurements are independent and identically distributed random variables having a common mean ? (the actual diameter) and a common variance of 4 nm. Please estimate the number of measurements he needs to perform so that the average value is accurate to within 0.5 nm, with probability at least 0.95, based on Central Limit Theorem.

Answer 1

Solution :

Given that,

variance = 2 = 4

Population standard deviation = = 2 = 4 = 2

Margin of error = E = 0.5

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96  

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

n = [1.96 *2 / 0.5]2

n = 61.46

Sample size = n = 62