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1.    1. Given the sample data.x:2616192415(a) Find the range.[removed](b) Verify that Σx = 100 and Σx2 = 2094.Σx[removed]Σx2[removed](c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s2 and sample standard deviation s. (Enter your answers to one decimal place.)s2[removed]s[removed](d) Use the defining formulas to compute the sample variance s2 and sample standard deviation s. (Enter your answers to one decimal place.)s2[removed]s[removed](e) Suppose the given data comprise the entire population of all x values. Compute the population variance σ2 and population standard deviation σ. (Enter your answers to one decimal place.)σ2[removed]σ[removed]2. Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.9 minutes and a standard deviation of 1.5 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)(a) the response time is between 5 and 10 minutes[removed](b) the response time is less than 5 minutes[removed](c) the response time is more than 10 minutes[removed]3. Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 69 and estimated standard deviation σ = 26. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)[removed](b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.[removed]The probability distribution of x is approximately normal with μx = 69 and σx = 18.38.[removed]The probability distribution of x is approximately normal with μx = 69 and σx = 13.00.    [removed]The probability distribution of x is approximately normal with μx = 69 and σx = 26.[removed]The probability distribution of x is not normal.What is the probability that x < 40? (Round your answer to four decimal places.)[removed](c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)[removed](d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)[removed](e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?[removed]Yes[removed]NoExplain what this might imply if you were a doctor or a nurse.[removed]The more tests a patient completes, the stronger is the evidence for excess insulin.[removed]The more tests a patient completes, the stronger is the evidence for lack of insulin.    [removed]The more tests a patient completes, the weaker is the evidence for lack of insulin.[removed]The more tests a patient completes, the weaker is the evidence for excess insulin.

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