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.
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?
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