The scores of a recent standardized test taken by finance majors at a four-year college had an approximately normal distribution with a mean of 225 and a standard deviation of 18. Determine the probability to the nearest integer that a randomly selected test scored between 200 and 245.(1 point)

Question

The probability that finance majors scored between 200 and 245 is
%.

Answer 1

To find the probability that a randomly selected test score is between 200 and 245, we need to use the z-score formula and then use a z-table to find the probabilities.

First, find the z-scores for both 200 and 245:
z1 = (200 - 225) / 18 = -1.39
z2 = (245 - 225) / 18 = 1.11

Now, we can use the z-table to find the probabilities associated with these z-scores:
P(z < -1.39) = 0.0823
P(z < 1.11) = 0.8686

Finally, subtract the probability of z < -1.39 from the probability of z < 1.11 to find the probability that a randomly selected test score is between 200 and 245:
0.8686 - 0.0823 = 0.7863

So, the probability that a randomly selected test score is between 200 and 245 is approximately 79%.