LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 300 and 600. Round your answer to four decimal places.
A)0.5907
B) 0.8185
C) 0.2954
D) 0.1815
E) 0.8175

Question

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 300 and 600. Round your answer to four decimal places. ​
A)0.5907
B) 0.8185
C) 0.2954
D) 0.1815
E) 0.8175

Quizplus · Accepted Answer

We can use the z-score formula to standardize the scores:
z = (x - mu) / sigma

where x is the score, mu is the mean, and sigma is the standard deviation.

For a score of 300:
z = (300 - 500) / 100 = -2

For a score of 600:
z = (600 - 500) / 100 = 1

Using a standard normal distribution table, we can find the probabilities associated with these z-scores:
P(z < -2) = 0.0228
P(z < 1) = 0.8413

To find the probability between 300 and 600, we can subtract the probability of getting a score below 300 from the probability of getting a score below 600:
P(300 < x < 600) = P(z < 1) - P(z < -2) = 0.8413 - 0.0228 = 0.8185

Therefore, the probability that a randomly chosen test taker will score between 300 and 600 is 0.8185, or approximately 0.82 when rounded to four decimal places. The best choice is B.

LSAT Test Scores Are Normally Distributed with a Mean of 500