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Suppose we have taken a sample of size 13 from a population that is normally distributed with population variance 6. We find that the sample mean is 80, and the sample variance is 7. Calculate the value of % based on the formula for the sampling distribution of S. Round your answer to 3 decimals. Find the probability that the sample variance is less than 7. Round your answer to 4 decimals.Suppose we have taken a sample of size ll] from a population that is normally distributed with population variance 'F. We find that the sample mean is El], and the sample variance is 1?. Calculate the value of 12 based on the formula for the sampling distribution of 32. Round your answer to 3 decimals. Find the probability that the sample variance is greater than 12. Round your answer to 4 decimals. Suppose you have a normally distributed population such that or2 = 1". Using the sampling distribution of 52, we find that from a random sample of size in. = 13, x2 = 2.5?. Does our population variance seem reasonable? Note: We 1vvill consider our population variance reasonable if our 1:2 value falls within the interval [x2035 {if}: famsldi- Part 1: Find the chi-square values. x_9?5[df} = [Round to 3 decimals.) Xumldf} = [Round to 3 decimals] Suppose you have a normally distributed population such that 0'2 = 3. Using the sampling distribution of 32, we find that from a random sample of size n = 1D, x2 = 2.?86. Does our population variance seem reasonable? Note: We will consider our population variance reasonable if our 1:2 value falls within the interval [XEELWE {if}: awsldl Part 1: Find the chi-square values. fmdf} = [Round to 3 decimals.) quzdf} = [Round to 3 decimals.)