standard deviation

Question

A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of eight ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain.

BIG Corporation would like to estimate the mean amount of coffee, 

μ

, dispensed per cup by this machine. BIG will choose a random sample of cup amounts dispensed by this machine and use this sample to estimate μ

. Assuming that the standard deviation of cup amounts dispensed by this machine is 0.40

 ounces, what is the minimum sample size needed in order for BIG to be 90%

 confident that its estimate is within 0.07

 ounces of μ

?Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).

(If necessary, consult a list of formulas.)

Answer 1

Hi Aubree,

The formula for sample size calculations like this is:

n=z_a/2*sigma²/E²

Let's break this down:

z_a/2=z-critical value based on our confidence level

sigma=standard deviation

E=acceptable error

Let's assign values for this problem:

z_a/2=1.645, z critical value for 90% confidence--you may want to memorize.

sigma=0.40

E=0.07

Substituting:

n=(1.645*0.40²)/0.07²

n=53.71, rounded

n=54

I hope this helps.