Question

In a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.3. Answer parts (a)-(d) below.(a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 487.The probability that a randomly selected medical student who took the test had a total score that was less than 487 is(Round to four decimal places as needed.)(b) Find the probability that a randomly selected medical student who took the test had a total score that was between 499 and 512.The probability that a randomly selected medical student who took the test had a total score that was between 499 and 512 is(Round to four decimal places as needed.)(c) Find the probability that a randomly selected medical student who took the test had a total score that was more than 527.The probability that a randomly selected medical student who took the test had a total score that was more than 527 is(Round to four decimal places as needed.)(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

Answer 1

First, we will find the z-score associated with a score of 487

(x – μ) / σ = (500-487)/10.3 =13/10.3 = 1.26213

Then P = 0.8962 according to the z-table

which is the answer to a part