The GRE is widely used to help predict the performance of applicants to graduate schools. The range of possible scores on a GRE is 200 to 900. The psychology department at a university finds that the students in their department have scores with a mean of 544 and standard deviation of 103. a. Find the probability that a student in the psychology department has a score less than 480. b. Find the probability that a student in the psychology department has a score between 480 and 730.

a) 26.76% probability that a student in the psychology department has a score less than 480.

b) 69.73% probability that a student in the psychology department has a score between 480 and 730.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we haev that:

a. Find the probability that a student in the psychology department has a score less than 480.

This is the pvalue of Z when X = 480. So

has a pvalue of 0.2676.

26.76% probability that a student in the psychology department has a score less than 480.

b. Find the probability that a student in the psychology department has a score between 480 and 730.

This probability is the pvalue of Z when X = 730 subtracted by the pvalue of Z when X = 480.

X = 730

has a pvalue of 0.9649.

X = 480

has a pvalue of 0.2676.

0.9649 - 0.2676 = 0.6973

69.73% probability that a student in the psychology department has a score between 480 and 730.

b

step-by-step explanation: