Work on the following questions below.

Question:

The outlet stream of a continuous chemical reactor is sampled every thirty minutes and titrated. Extensive records of normal operation show the concentration of component A in this stream is approximately normally distributed with mean 41.2 g/L and standard deviation 0.90 g/L.?

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a) What is the probability that the concentration of component A in this stream will be more than 42.3 g/L??

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b) Five determinations of concentration of component A are made. If the mean of these five concentrations is more than 42.3 g/L, action is taken. What is the level of significance associated with this test??

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c) State the null hypothesis and the alternative hypothesis that fit the test described in part (b).?

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d) The test in part (b) is applied. Now suppose the true mean has changed to 43.5 g/L with no change in standard deviation. What is the probability of a Type II error??

Question '14 C: Mark this question Which of the following statements is true? 0 The Central Limit Theorem is applicable only for data sets comprising exactly thirty samples. 0 The Central Limit Theorem is applicable only for data sets comprising thirty or more samples. 0 The Central Limit Theorem is applicable only for data sets comprising more than thirty samples. 0 The Central Limit Theorem is applicable only for data sets comprising less than thirty samples. [4] Consider the following system of equations: 6r 2y + 10 2x + 12 (1) I + 2y 5 with the exact solution r = (1. 2.0)T. (a) Write down the Jacobi method corresponding (specifically) to this system. (b) Repeat part (a) for the Gauss-Seidel method. (c) Prove that the Jacobi and Gauss-Seidel iterations converge for this system.\fA sample of size n is taken from a population with an unknown distribution, with mean // and standard deviation O. Which of the following statements about the sample mean distribution is true? Select one: a. without Using the Central Limit Theorem, X approximately followsX - N H,- 02 n b. Using the Central Limit Theorem, Xexactly followsX - NCH, 02 n C. without Using the Central Limit Theorem, Xexactly followsX - Nu,- 02 n d. Using the Central Limit Theorem, X approximately followsX - Nu,- n7.2 The Central Limit Theorem for Sums 1. Central limit theorem for means {X}: 3. The condition for central limit theorem I The sample size should be at least .................... or the sample data should come from a [t the sample size is 2 3-D, then X has a normal distribution even if the data values (X) of the population do not follow a normal distribution