A bottled water distributor wants to estimate the amount of water contained 1 ga

Question

A bottled water distributor wants to estimate the amount of water contained 1 gallon bottles purchased from a nationally known water bottling company The water in betting company's specifications state that the standard deviation of the amount of water is equal to 0.03 gallon. A random sample of 50 bottles is selected and the sample mean amount of water per 1-gallon bottle is 0.956 gallon. Complete parts (a)through (d). a Construct a 9% confidence interval estimate for the population mean amount of water included in a1-gallon bottle. Lessthanorequalto mu lessthanorequalto (Round to five decimal places as needed.)

Explanation / Answer

Solution:

a) Compute the sample mean and population standard deviation:
x = 0.956 = 0.03

Using NORM.INV(0.005,0,1) or a table we nd that Z/2 = Z0.005 = 2.576. Now, calculating the condence interval:
  
x = x + Z/2 /n = 0.956 + 2.576 * 0.03/50 = 0.9669
x = x - Z/2 /n = 0.956 - 2.576 * 0.03/50 = 0.9451
C.I = x ± Z/2 /n = [0.9451, 0.9669]
0.9451 0.9669

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