LSAT test scores are normally distributed with a mean of 155 and a standard deviation of 7. Find the probability that a randomly chosen test-taker will score 148 or lower.

Question

You may need to use the appropriate appendix table or technology to answer this question.

LSAT test scores are normally distributed with a mean of 155 and a standard deviation of 7. Find the probability that a randomly chosen test-taker will score 148 or lower. (Round your answer to four decimal places.)

Answer 1

the empirical rule states that 68.3% of the scores fall within 1 standard deviation of the mean. 155-148= 7 = 1 standard deviation below the mean

1-.683 = .317. divide by 2. .317/2 = 0.1585 = 15.85% fall below 147

Or go to the z tables, in a statistics textbook or online, or use a calculator with statistics functions for z scores. 0.1587 should be the probability for z=-1.000

0.1587 = 15.87% probability of less than 147 with mean 155 and standard deviation 7

Answer: 0.1587 or 15.87%

Just google "z tables" and look for z=-1, and the 1st column's entry should read .1587, that's for a z score of -1.000