Answer :
Final answer:
To find P71, we need to find the z-score corresponding to the bottom 71% and convert it back to the original score using the mean and standard deviation.
Explanation:
To find P71, which is the score separating the bottom 71% from the top 29%, we need to find the z-score corresponding to that percentile and then convert it back to the original score using the mean and standard deviation. First, we find the z-score using the inverse normal distribution table or calculator. The z-score corresponding to the bottom 71% is approximately -0.483, rounded to three decimal places.
Next, we convert the z-score to the original score using the formula: x = mean + (z-score * standard deviation). Substituting the values, x = 101.2 + (-0.483 * 49.1) = 76.138, rounded to three decimal places. Therefore, P71 is approximately 76.138.
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