WoW: In the computer game World of Warcraft, some of the strikes are critical strikes, which do more damage. Assume that the probability of a critical strike is the same for every attack, and that attacks are independent. During a particular fight, a character has 238 critical strikes out of 599 attacks.
Part: $0 / 3$
Part 1 of 3
(a) Construct a $98 \%$ confidence interval for the proportion of strikes that are critical strikes. Round the answer to at least three decimal places. A $98 \%$ confidence interval for the proportion of strikes that are critical strikes is $\square< p< \square$.

Step 1 ：First, we need to calculate the sample proportion (p̂). This is done by dividing the number of critical strikes (238) by the total number of attacks (599).

Step 2 ：Next, we calculate the standard error (SE) using the formula \( \sqrt{(p̂*(1-p̂))/n} \), where n is the total number of attacks.

Step 3 ：Then, we calculate the confidence interval using the formula \( p̂ ± Z*SE \). Here, Z is the z-score corresponding to our desired confidence level of 98%, which is approximately 2.33.

Step 4 ：Substituting the values we have, we get \( p̂ = 0.397 \), \( SE = 0.020 \), \( CI_{lower} = 0.351 \), and \( CI_{upper} = 0.444 \).

Step 5 ：Final Answer: A 98% confidence interval for the proportion of strikes that are critical strikes is \( \boxed{0.351}