Question

Suppose that, in a certain population, the distribution of GRE scores is normal with mean μ=600 and standard deviation s=80. What is the probability of a score less than 450 or greater than 750?

Answer 1

The probability of a GRE score being less than 450 or greater than 750 is calculated by finding the corresponding z-scores for 450 and 750, looking up these z-scores in a normal distribution table, and summing the probabilities.

Step-by-step explanation:

To find the probability of a GRE score being less than 450 or greater than 750, we can use the concept of the standard normal distribution. Since the distribution of GRE scores is given as normal with mean μ=600 and standard deviation σ=80, we need to calculate the corresponding z-scores for 450 and 750.

To find the z-score for a GRE score of 450:
z = (450 - μ) / σ = (450 - 600) / 80 = -150 / 80 = -1.875.

To find the z-score for a GRE score of 750:
z = (750 - μ) / σ = (750 - 600) / 80 = 150 / 80 = 1.875.

We then look up these z-scores in a standard normal distribution table or use a calculator with a normal distribution function to find the probabilities for the z-scores:

• The probability of a score less than 450 (z < -1.875)
• The probability of a score greater than 750 (z > 1.875)

The total probability is the sum of these two probabilities.