Final answer:
An individual needs to score approximately 321 on the exam to be in the highest 5%, calculated using a z-score of 1.645 and the given mean and standard deviation.
Step-by-step explanation:
To find out how high an individual must score to be in the highest 5% of an exam that is normally distributed, we need to use the concept of z-scores. A z-score represents the number of standard deviations a data point is from the mean. For a normally distributed set of exam scores with a mean of 235 and a standard deviation of 52, being in the highest 5% correlates to having a z-score that falls at the 95th percentile.
Typically, the z-score for the 95th percentile is approximately 1.645. To find the corresponding exam score, we can use the formula score = mean + (z-score × standard deviation). Plugging in the values, we get:
score = 235 + (1.645 × 52)
score = 235 + 85.54
score ≈ 320.54
Therefore, an individual must score approximately 321 to be in the highest 5% of exam scores.