Mathematics

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 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
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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 xHint: 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.)
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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?

[removed]Yes[removed]No

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.

 

 

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