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1.    1. Given the sample data.

(a) Find the range.
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(b) Verify that Σx = 100 and Σx² = 2094.

(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.)

(d) Use the defining formulas to compute the sample variance s² and sample standard deviation s. (Enter your answers to one decimal place.)

(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.)

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
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(b) the response time is less than 5 minutes
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(c) the response time is more than 10 minutes
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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.)
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(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 μ_x = 69 and σ_x = 18.38.[removed]The probability distribution of x is approximately normal with μ_x = 69 and σ_x = 13.00.    [removed]The probability distribution of x is approximately normal with μ_x = 69 and σ_x = 26.[removed]The probability distribution of x is not normal.

What is the probability that x < 40? (Round your answer to four decimal places.)
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(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
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(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)
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(e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?

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Explain 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.