Question

question 18 (bonus) (1 point)
the act scores from students in a state were analyzed and found to have a mean of 24.5 and a standard deviation of 3.15.
____ percent of students scored below a 27 on the act?
round the z - score to two decimal places if needed. round your answer to two decimal places. do not include the % sign in your answer.
your answer:

answer
question 19 (bonus) (1 point)
the act scores from students applying to uofa was analyzed and found to be approximately a normal distribution with a mean of 24 and a standard deviation of 2.3.
____ percent of students scored above a 20.8 on the act who applied to uofa (this is the average national score for all test takers in 2017)?
round the z - score to two decimal places if needed. round your answer to two decimal places. do not include the % sign in your answer.

Explanation:

Step1: Calculate the z - score for Question 18

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 27\), \(\mu=24.5\), and \(\sigma = 3.15\).

$$z=\frac{27 - 24.5}{3.15}=\frac{2.5}{3.15}\approx0.79$$

Using the standard normal distribution table, the area to the left of \(z = 0.79\) is \(0.7852\).

Step2: Calculate the z - score for Question 19

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 20.8\), \(\mu = 24\), and \(\sigma=2.3\).

$$z=\frac{20.8 - 24}{2.3}=\frac{- 3.2}{2.3}\approx - 1.39$$

Using the standard normal distribution table, the area to the left of \(z=-1.39\) is \(0.0823\). The area to the right (students who scored above) is \(1 - 0.0823=0.9177\).

Answer:

Question 18: \(78.52\)
Question 19: \(91.77\)