Question

The average MCAT score follows a Normal distribution, with a mean of μ = 508 and a standard deviation of σ = 8. What is the probability that the mean MCAT score of 100 randomly selected people will be more than 510? (2 points)

it is not 0.4013

Answer 1

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%.