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Math  /  Statistics

QuestionQuestion 19 1 pts
Evaluate the following expression at the values xˉ=89.2,μ=89,σ=0.77\bar{x}=89.2, \mu=89, \sigma=0.77, and n=153n=153 xˉ−μσn\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}
Enter your answer as a decimal rounded to four decimal places.

Studdy Solution

STEP 1

1. The expression to be evaluated is xˉ−μσn\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}.
2. The values given are xˉ=89.2\bar{x} = 89.2, μ=89\mu = 89, σ=0.77\sigma = 0.77, and n=153n = 153.
3. The problem involves basic arithmetic and square root calculations.

STEP 2

1. Calculate the numerator xˉ−μ\bar{x} - \mu.
2. Calculate the denominator σn\frac{\sigma}{\sqrt{n}}.
3. Divide the numerator by the denominator.
4. Round the result to four decimal places.

STEP 3

Calculate the numerator xˉ−μ\bar{x} - \mu.
xˉ−μ=89.2−89=0.2 \bar{x} - \mu = 89.2 - 89 = 0.2

STEP 4

Calculate the denominator σn\frac{\sigma}{\sqrt{n}}.
n=153 \sqrt{n} = \sqrt{153}

STEP 5

Compute 153\sqrt{153}.
153≈12.3693 \sqrt{153} \approx 12.3693

STEP 6

Now, calculate σn\frac{\sigma}{\sqrt{n}}.
σn=0.7712.3693≈0.0623 \frac{\sigma}{\sqrt{n}} = \frac{0.77}{12.3693} \approx 0.0623

STEP 7

Divide the numerator by the denominator.
xˉ−μσn=0.20.0623≈3.2104 \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} = \frac{0.2}{0.0623} \approx 3.2104

STEP 8

Round the result to four decimal places.
≈3.2104 \approx 3.2104
Solution: The value of the expression evaluated at the given values is approximately 3.21043.2104.

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