res for the California Peace Officer Standards and Training test are normally distributed, with of 50 and a standard deviation of 9 . An agency will only hire applicants with scores in the top That is the lowest score an applicant can earn and still be eligible to be hired by the agency? oints) The lowest score is

Step 1 ：The mean score for the California Peace Officer Standards and Training test is \( \mu = 50 \)

Step 2 ：The standard deviation of the scores is \( \sigma = 9 \)

Step 3 ：The agency will only hire applicants with scores in the top 5%, which corresponds to the \( 95^{th} \) percentile

Step 4 ：To find the lowest score for the top 5%, we need to find the z-score that corresponds to the \( 95^{th} \) percentile

Step 5 ：The z-score for the \( 95^{th} \) percentile is \( z = 1.6448536269514722 \)

Step 6 ：We use the z-score formula to find the lowest score: \( X = \mu + z \cdot \sigma \)

Step 7 ：Substitute the known values into the formula: \( X = 50 + 1.6448536269514722 \cdot 9 \)

Step 8 ：Calculate the lowest score: \( X = 64.80368264256325 \)

Step 9 ：Round the lowest score to the nearest whole number: \( X = 65 \)

Step 10 ：The final answer is \(\boxed{65}\)