Question

Suppose student test scores for a nationwide standardized test have an unknown distribution with a mean of 259 and a standard deviation of 33 points. A sample of size n=38 is randomly taken from the population and the mean is taken. What is the probability that the resulting mean is more than 264.3 points?

Answer 1

To find the probability that the resulting mean is more than 264.3 points, we need to calculate the z-score and then find the corresponding probability using the standard normal distribution.

Step-by-step explanation:

To find the probability that the resulting mean is more than 264.3 points, we need to calculate the z-score and then find the corresponding probability using the standard normal distribution.

1. Calculate the z-score: z = (x - μ) / (σ / √n) = (264.3 - 259) / (33 / √38) = 1.257
2. Find the corresponding probability using the standard normal distribution table or a calculator: P(z > 1.257) = 1 - P(z < 1.257)
3. Lookup the z-score in the standard normal distribution table: P(z < 1.257) = 0.8938
4. Calculate the probability: P(z > 1.257) = 1 - 0.8938 = 0.1062, or 10.62%