Question 1180147
Here's how to calculate the confidence interval and interpret it:

**1. Calculate the Sample Mean (x̄):**

Add all the tongue flick counts and divide by the number of lizards (17):

x̄ = (425 + 510 + 629 + 236 + 654 + 200 + 710 + 276 + 633 + 501 + 811 + 332 + 424 + 674 + 676 + 662 + 694) / 17
x̄ = 8741 / 17
x̄ ≈ 514.18 tongue flicks

**2. Identify Given Information:**

* Sample size (n) = 17
* Population standard deviation (σ) = 190
* Confidence level = 90%

**3. Find the Critical Z-Value:**

For a 90% confidence level, α = 1 - 0.90 = 0.10.  α/2 = 0.05. We need to find the z-score that corresponds to an area of 0.95 (1 - 0.05) in the standard normal distribution. This z-value is approximately 1.645.

**4. Calculate the Margin of Error (E):**

E = z * (σ / √n)
E = 1.645 * (190 / √17)
E ≈ 1.645 * (190 / 4.123)
E ≈ 1.645 * 46.08
E ≈ 75.71 tongue flicks

**5. Construct the Confidence Interval:**

Lower Bound = x̄ - E = 514.18 - 75.71 ≈ 438.47 tongue flicks
Upper Bound = x̄ + E = 514.18 + 75.71 ≈ 589.89 tongue flicks

Therefore, the 90% confidence interval is approximately (438.47, 589.89).

**Interpretation:**

We are 90% confident that the true mean number of tongue flicks per 20 minutes for all juvenile common lizards when exposed to viper snake chemical cues is between 438.47 and 589.89 tongue flicks.  This means that if we were to repeat this study many times and calculate a 90% confidence interval each time, 90% of those intervals would contain the true population mean.