Question

In a recent year, the tolal scores for a certain standardized tost wore normally distributed, with a mean of 500 and a standard deviation of 10.7 . Find the probabily that a randomly selected medical student who took the test had a total score that was less than 489

Answer 1

To find the probability that a randomly selected medical student who took the test had a total score that was less than 489, we can calculate the z-score and use the standard normal distribution table.

Step-by-step explanation:

To find the probability that a randomly selected medical student who took the test had a total score that was less than 489, we need to calculate the z-score and then find the corresponding probability from the standard normal distribution table.

The formula to calculate the z-score is: z = (X - μ) / σ, where X is the value we want to find the probability for, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

In this case, X = 489, μ = 500, and σ = 10.7. Plugging these values into the formula, we get: z = (489 - 500) / 10.7 = -1.028.

Now, we can look up the corresponding probability for a z-score of -1.028 in the standard normal distribution table. From the table, we find that the probability is approximately 0.1503. Therefore, the probability that a randomly selected medical student who took the test had a total score less than 489 is 0.1503 or 15.03% (rounded to two decimal places).