To find the minimum score needed to be in the top 7%, we need to find the score that corresponds to the 93rd percentile, since the top 7% is the complement of the bottom 93%.
Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 93rd percentile, which is approximately 1.44. This means that a score of 1.44 standard deviations above the mean corresponds to the 93rd percentile.
To find the actual score, we can use the formula:
z = (x - μ) / σ
where z is the z-score, x is the actual score, μ is the mean, and σ is the standard deviation. Solving for x, we get:
x = z * σ + μ
= 1.44 * 6.1 + 76.4
= 85.084
So, the minimum score needed to be in the top 7% is approximately 85.084 points.