Question

Consider the following two distributions for GRE scores: N(μ=149;σ=7) for the verbal part of the exam and N(μ=154;σ=7.76) for the quantitative part. Use this information to find the probability that a student scores 160 or higher on the verbal part.

Answer 1

To find the probability that a student scores 160 or higher on the verbal part of the GRE exam, calculate the z-score and use the standard normal distribution table.

Step-by-step explanation:

To find the probability that a student scores 160 or higher on the verbal part of the GRE exam, we need to calculate the z-score and then use the standard normal distribution table.

The formula for calculating the z-score is: z = (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation.

In this case, x = 160, μ = 149, and σ = 7. Plugging these values into the formula, we get: z = (160 - 149) / 7 = 1.57.

Now, we can use the standard normal distribution table to find the probability associated with a z-score of 1.57. Looking up the z-score in the table, we find that the corresponding probability is approximately 0.9418.

Therefore, the probability that a student scores 160 or higher on the verbal part of the GRE exam is approximately 0.9418, or 94.18%.