# Mathematics

1. 1. Given the sample data.

x: |
26 | 16 | 19 | 24 | 15 |

(a) Find the range.

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(b) Verify that Σ*x* = 100 and Σ*x*^{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*

*= 18.38.[removed]The probability distribution of*

_{x}*x*is approximately normal with

*μ*

*= 69 and*

_{x}*σ*

*= 13.00. [removed]The probability distribution of*

_{x}*x*is approximately normal with

*μ*

*= 69 and*

_{x}*σ*

*= 26.[removed]The probability distribution of*

_{x}*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.