1. 1. Given the sample data.
x: |
26 |
16 |
19 |
24 |
15 |
(a) Find the range.
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(b) Verify that Σx = 100 and Σx^{2} = 2094.
Σx |
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Σx^{2} |
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(c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s^{2} and sample standard deviation s. (Enter your answers to one decimal place.)
s^{2} |
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s |
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(d) Use the defining formulas to compute the sample variance s^{2} and sample standard deviation s. (Enter your answers to one decimal place.)
s^{2} |
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s |
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(e) Suppose the given data comprise the entire population of all x values. Compute the population variance σ^{2} and population standard deviation σ. (Enter your answers to one decimal place.)
σ^{2} |
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σ |
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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.