A beverage company uses a machine to fill one-liter bottles with water (see figu

Question

A beverage company uses a machine to fill one-liter bottles with water (see figure). Assume that the population of volumes is normally distributed. (a)The company wants to estimate the mean volume of water the machine is putting in the bottles within 1 milliliter. Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 4 milliliters. (b) Repeat part (a) using an error tolerance of 3 milliliters. Which error tolerance requires a larger sample size? Explain. (a) The minimum sample size required for an error tolerance of 1 milliliter is bottles. (Round up to the nearest integer.)

Explanation / Answer

Solution:

A) For a normal distribution with 90% confidence , the z-value is 1.645
Sample size n = [z sd /e]^2
z=1.645
sd=4
error = 1

n = [ (1.645)(4)/1]^2 =43.2964
n=44 samples

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