The probability that the mean MCAT score of 100 randomly selected people will be more than 510 is approximately 0.0062 or 0.62%.
To find the probability that the mean MCAT score of 100 randomly selected people will be more than 510, you can use the properties of the Central Limit Theorem.
Given:
Mean (μ) = 508
Standard deviation (σ) = 8
Sample size (n) = 100
Firstly, find the standard error of the mean (SEM) using the formula:
SEM= 8/ √100 = 8/10 =0.8
Now, convert the value of 510 to a z-score using the formula:
z= X−μ/ SEM
z= 510−508/0.8 = 2/ 0.8 =2.5
Next, find the probability using a standard normal distribution table or calculator. We want to find the probability of getting a z-score greater than 2.5.
From a standard normal distribution table, the probability of getting a z-score greater than 2.5 is approximately 0.0062 or 0.62%.
Therefore, the probability that the mean MCAT score of 100 randomly selected people will be more than 510 is approximately 0.0062 or 0.62%.