Question

eric and joseph were completing their homework and came across a problem in which they had different answers. the problem was: angela is going to take a standardized test. the passing score on this test is 220. the mean score on the test is 230 with a standard deviation of 20. find the probability that she will score less than 220 points on the test. whose answer is correct?

eric	joseph
z - score from table is 0.3085	z - score from the table is 0.6915
probability is 30.85%	probability is 69.15%

josephs answer is correct. eric found the wrong z - score.
erics answer is correct. joseph found the wrong z - score.
both joseph and erics answers are correct. there is more than one answer to this problem.
neither answer is correct. eric was closer because all he had to do next was add 0.5 to his answer and get 0.8085, which is 80.85%.

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. We want to find the probability that $x = 220$, $\mu=230$, and $\sigma = 20$.

Step2: Calculate the z - score

$z=\frac{220 - 230}{20}=\frac{- 10}{20}=-\frac{1}{2}=-0.5$

Step3: Use the standard normal distribution table

Looking up the z - score of $- 0.5$ in the standard - normal distribution table, the corresponding probability is $0.3085$ or $30.85\%$. Eric calculated the z - score correctly and used the table correctly.

Answer:

Eric's answer is correct. Joseph found the wrong z - score.