A random sample of size n=51 is taken from a finite population of size N=442 with mean =233 and variance 2=443. [You may find it useful to reference the z table.] a-1. Is it necessary to apply the finite population correction factor? Yes No a.2. Calculate the expected value and the standard error of the sample mean.(Round "expected value" to a whole number and "standard error" to 4 decimal places.) b. What is the probability that the sample mean is less than 219 ? (Round final answer to 4 decimal places.) b. What is the probability that the sample mean is less than 219 ? (Royund final answer to 4 decimal places.) c. What is the probability that the sample mean lies between 224 and 244 ? (Round final answer to 4 decimal place: Random samples of size n=400 are taken from a population with p=0.10. a. Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the p chart. (Round the value for the centerline to 2 decimal places and the values for the UCL and LCL to 3 decimal places.) b. Suppose six samples of size 400 produced the following sample proportions: 0.06,0.11,0.09,0.08,0.14, and 0.16 . Is the production process under control