Test scores for a standardized math test follow a normal distribution with a mean of 73 and a standard deviation of 8. A random sample of 23 students took this math test. What is the probability that the average score of the 23 students falls above 75?
A)

Question

Test scores for a standardized math test follow a normal distribution with a mean of 73 and a standard deviation of 8. A random sample of 23 students took this math test. What is the probability that the average score of the 23 students falls above 75?
A) < 0.0001
B) 0.1151
C) 0.4013
D) 0.8849

Quizplus · Accepted Answer

To find the probability that the average score of the 23 students falls above 75, we use the formula for the standard error of the mean: $SE = \frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the standard deviation and $n$ is the sample size. Here, $\sigma = 8$ and $n = 23$, so $SE = \frac{8}{\sqrt{23}}$. Next, we calculate the z-score for a sample mean of 75: $z = \frac{\bar{x} - \mu}{SE}$, where $\bar{x} = 75$ and $\mu = 73$. Plugging in the values, we find the z-score and then use the standard normal distribution to find the probability of a z-score being above this value. The calculation yields a probability of 0.1151, indicating that there's an 11.51% chance the average score of the 23 students is above 75.

Test Scores for a Standardized Math Test Follow a Normal