A bottled water distributor wants to estimate the amount of water contained in -gallon bottles purchased from a nationally known water botting company. The water botting company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon. a. Construct a 99 % confidence interval estimate for the population mean amount of water included in a 1-gallon bottle. b. On the basis of these results, do you think that the distributor has a right to complain to the water botting company about the amount of water that the bottles contain? Why? c. must you assume that the population amount of water per bottle is normally distributed here? Explain. d. Construct a 95% confidence interval estimate. How doe this change your answer to (b)?
A bottled water distributor wants to estimate the amount of water contained in -gallon bottles purchased from a nationally known water botting company. The water botting company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon. a. Construct a 99 % confidence interval estimate for the population mean amount of water included in a 1-gallon bottle. b. On the basis of these results, do you think that the distributor has a right to complain to the water botting company about the amount of water that the bottles contain? Why? c. must you assume that the population amount of water per bottle is normally distributed here? Explain. d. Construct a 95% confidence interval estimate. How doe this change your answer to (b)?
Solution Summary: The author calculates a confidence interval of 99% for the population mean of the amount of water in bottles.
A bottled water distributor wants to estimate the amount of water contained in -gallon bottles purchased from a nationally known water botting company. The water botting company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon.
a. Construct a
99
%
confidence interval estimate for the population mean amount of water included in a 1-gallon bottle.
b. On the basis of these results, do you think that the distributor has a right to complain to the water botting company about the amount of water that the bottles contain? Why?
c. must you assume that the population amount of water per bottle is normally distributed here? Explain.
d. Construct a 95% confidence interval estimate. How doe this change your answer to (b)?
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
A well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected.
a) Calculate the percentage of components that get rejected.
b) In a manufacturing run of 1000 units, how many are expected to be rejected?
c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.
5. Let X and Y be independent random variables and let the superscripts denote
symmetrization (recall Sect. 3.6). Show that
(X + Y) X+ys.
8. Suppose that the moments of the random variable X are constant, that is, suppose
that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.
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