Question

question 2
andrew is taking the act and is hoping to make a 28 on the mathematics portion. the mean score on the mathematics portion of the act is 20.5 with a standard deviation of 5.5. he found his probability to be 94.84%. is he correct?
he is incorrect. the z - score is - 1.30, which makes the probability 8.36%
he is correct. the z - score is - 1.30, which makes the probability 1.64%
he is correct. the z - score is 1.30, which makes the probability 91.31%
he is incorrect. the z - score is 1.30, which makes the probability 91.31%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 28$ (Andrew's target score), $\mu=20.5$ (mean score) and $\sigma = 5.5$ (standard deviation). So, $z=\frac{28 - 20.5}{5.5}=\frac{7.5}{5.5}\approx1.36$.

Step2: Find the probability

Using a standard normal distribution table or calculator, the cumulative - distribution function value for $z = 1.36$ is approximately $0.9131$ or $91.31\%$.

Answer:

He is incorrect. The z - score is 1.36, which makes the probability 91.31%. So the answer is the last option: He is incorrect. The z - score is 1.36, which makes the probability 91.31%.