Questions: Determine the value of Z using the formula Z=((x-μ)/√n)/(1/n) given x̄=23, μ=28.4, σ=11, n=85. Round the answer to two decimal places.

Solution Steps

To find the standard error \( SE \), we use the formula:

\[ SE = \frac{\sigma}{\sqrt{n}} \]

Substituting the given values:

\[ SE = \frac{11}{\sqrt{85}} \]

Calculating this gives:

\[ SE \approx 1.1931 \]

Next, we calculate the Z-score \( Z \) using the formula:

\[ Z = \frac{\bar{x} - \mu}{SE} \]

Substituting the values we have:

\[ Z = \frac{23 - 28.4}{1.1931} \]

Calculating this gives:

\[ Z \approx -4.52596 \]

Finally, we round the Z-score to two decimal places:

\[ Z \approx -4.53 \]

Final Answer