Please show work or show the formula used and answers as a numerical values

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(a) Fill in the blank spaces and spaces within parentheses ( ) by writing suitable symbols or values. Let X be the sample mean of size n from a population with mean / and variance of. Then, un- der certain conditions, the sampling distribution of X is with mean and variance The distribution of X - ( Z is State two conditions each of which by itself will make the above statement to be valid. (i) (ii)The breaking strength of yarn used in manufacturing drapery material is required to be at least 100 psi. Past experience has indicated that breaking strength is normally distributed with (population) standard deviation, o = 2 psi. Suppose we wanted to estimate the (population) mean breaking strength, /. A random sample of 9 specimens is tested, and the average breaking strength was found to be 98 psi. (a) Give the point estimate for ji.(b) Find the estimated standard error of the point estimate. (c) Find a 95% confidence interval for the true mean breaking strength, /. (Note: we cover only 2-sided confidence intervals in the course.)The elasticity of a polymer is affected by the concentra- tion of a reactant. When low concentration is used, the true mean elasticity is 50, and when high concentration is used the mean elasticity is 52. The standard deviation of elasticity is 4, regardless of concentration. If two random samples of size 25 are taken, find the probability that 1