LSAT test scores are normally distributed with a mean of 490 and a standard deviation of 110. Find the probability that a randomly chosen test-taker will score between 320 and 600. (Round your answer to four decimal places.)
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z scores.
To find the probability that a randomly chosen test-taker will score between 320 and 600 on the LSAT, we will need to standardize the scores and then use the standard normal distribution.
Step 1: Standardize the scores
To standardize a score, we subtract the mean and then divide by the standard deviation. In this case, the mean is 490 and the standard deviation is 110. So, for a score of 320:
Z-score = (320 - 490) / 110 = -1.545
For a score of 600:
Z-score = (600 - 490) / 110 = 1.000
Step 2: Calculate the probability
Once we have the standardized scores, we can use a standard normal distribution table or a calculator to find the probabilities associated with those values.
Using a standard normal distribution table, we look up the probability corresponding to each Z-score:
For -1.545, the probability is 0.0622
For 1.000, the probability is 0.8413
Step 3: Calculate the probability between the scores
To find the probability between the scores, we subtract the smaller probability from the larger probability:
0.8413 - 0.0622 = 0.7791
So, the probability that a randomly chosen test-taker will score between 320 and 600 on the LSAT is 0.7791 (rounded to four decimal places).