Most graduate schools business require applicants from admission to take the Graduate Management Admission Council's GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviations 112. What is the probability of an individual scoring above 500 on the GMAT?
To solve this problem, we need to calculate the standard score (z-score) of an individual scoring above 500, using the formula:
z = (x - μ) / σ
where x is the raw score (500), μ is the mean (527), and σ is the standard deviation (112).
z = (500 - 527) / 112
z = -0.241
We can then use a standard normal distribution table (or a calculator with a normal distribution function) to find the probability of a z-score being less than -0.241, which is the same as the probability of a score above 500.
The table shows that the probability of a z-score less than -0.241 is 0.4066. Therefore, the probability of an individual scoring above 500 on the GMAT is:
P(x > 500) = P(z < -0.241) = 0.4066
This means that about 40.66% of individuals taking the GMAT will score above 500.