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The blood pressure of a person changes throughout the day. Suppose the systolic blood pressure of a person is measured 36 times over several days and the standard deviation of these measurements for the person is known to be σ = 10.0 mmHg. Let μ be the true average blood pressure for that person and let x = 85 be the average of the 36 measurements.

Find a two-sided 90% confidence interval for μ. One can be 90% confident that the true average blood pressure μ for that person is between a and b.

What is the value of a? Round your answer to the nearest 0.0001. 

The blood pressure of a person changes throughout the day. Suppose the systolic blood pressure of a person is measured 36 times over several days and the standard deviation of these measurements for the person is known to be σ = 8.1 mmHg. Let μ be the true average blood pressure for that person and let x = 82 be the average of the 36 measurements.

Find a lower-bound 90% confidence interval for μ. One can be 90% confident that the true average blood pressure μ for that person is at least 

Round your answer to the nearest 0.0001.

The blood pressure of a person changes throughout the day. Suppose the systolic blood pressure of a person is measured 36 times over several days and the standard deviation of these measurements for the person is known to be σ = 9.3 mmHg. Let μ be the true average blood pressure for that person and let x = 96 be the average of the 36 measurements.

Find a upper-bound 90% confidence interval for μ. One can be 90% confident that the true average blood pressure μ for that person is at most

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