Math Snap

STEP 1

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

STEP 2

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

STEP 3

Calculate the numerator $\bar{x} - \mu$.
$$\bar{x} - \mu = 89.2 - 89 = 0.2$$

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

Divide the numerator by the denominator.
$$\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} = \frac{0.2}{0.0623} \approx 3.2104$$

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