Homework SourseChapter 11 part 2 15 A manufacturing process produces bags o
Chapter 11 part 2.
15. A manufacturing process produces bags of cookies. The distribution of content weights of these bags is Normal with mean 15.0 oz and standard deviation 1.0 oz. We will randomly select n bags of cookies and weigh the contents of each bag selected.
Which of the following statements is true with respect to the sampling distribution of the sample mean, ?
A.If the sample size, n, increases, the standard deviation of will decrease.
B.According to the law of large numbers, if the sample size, n, increases, will tend to be closer to 15 ounces.
C.If the population standard deviation increases, the standard deviation of will increase.
D.All of the above.
16. The scores of individual students on the American College Testing (ACT) Program Composite College Entrance Examination have a Normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. What is the mean of the sampling distribution of the sample mean score for a random sample of 36 students?
A.1.0
C.3.1
B.6.0
D.18.6
What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students?
A.1.0
B. 3.1
C.6.0
D.18.6
What is the sampling distribution of the sample mean score for a random sample of 36 students?
A.Approximately Normal, but the approximation is poor.
B.Approximately Normal, and the approximation is good.
C.Exactly Normal.
D.Neither Normal nor non-Normal. It depends on the particular 36 students selected.
Box 1: Select the best answer
Box 2: Select the best answer
Box 3: Select the best answer
17. The weights of extra-large eggs have a Normal distribution with a mean of 1 oz and a standard deviation of 0.1 oz. What is the sampling distribution of the sample mean weight of the eggs in a randomly selected carton of a dozen eggs?
A.N(1, 0.029)
B.N(1, 0.1)
C.N(12, 0.1)
D.N(12, 1)
What is the probability that a carton of a dozen eggs weighs more than 13 oz?
A.0.0000
B.0.0019
C.0.1814
D.0.2033
Box 1: Select the best answer
Box 2: Select the best answer
19. In the construction industry, compressive strength of concrete is a crucial characteristic. Suppose for a particular residential construction job the concrete tested after 3 days should have a mean compression strength of = 3000 psi with a standard deviation of = 50 psi. It is known that compressive strength of concrete is Normally distributed. On a construction site, a sample of n = 5 specimens is selected and tested after 3 days. If the concrete has the desired characteristics, what is the probability that the sample mean will be larger than 3060 psi?
A.0.996
B.0.004
C.0.885
D.0.115
E.Unable to determine because the sample size n = 5 is much too small to rely on the Normal distribution for calculation of the required probability.
Box 1: Select the best answer
20. A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons. The manufacturer of this gasoline tank considers the largest 2% of these tanks too large to put on the market. How large does a tank have to be, to be considered too large?
A.15 gallons
B.15.31 gallons
C.15.72 gallons
D.16 gallons
What proportion of tanks will hold between 14.75 and 15.10 gallons of gas?
A.0.35
B.0.6563
C.0.6997
D.0.9833
If a simple random sample of four tanks is selected, and their capacities can be considered independent, what is the probability that all four will hold between 14.75 and 15.10 gallons of gas?
A.0.2397
B.0.6808
C.0.9084
D.2.7988
If four tanks are randomly selected, what is the probability that their average capacity will be between 14.75 and 15.10 gallons?
A.0.2397
B.0.6808
C.0.9084
D.0.9962
Box 1: Select the best answer
Box 2: Select the best answer
Solution
15) A
16) A
17) C
18) D
19) B
20) B
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