Question

suppose that at a certain school gpas of students are uniformly distributed between 1 and 4. approximate the probability that in a random sample of 25 students from this school, the sample mean gpa is greater than 3.0. your final answer should be a single number, but explain fully the justification for your approximation and the details of your calculation.

Answer 1

Calculating the z-score:
z = (3.0 - 2.5) / (0.866 / sqrt(25))
z = 0.5 / (0.866 / 5)
z ≈ 2.886

Now, we can use a standard normal distribution table or calculator to find the probability corresponding to a z-score of 2.886. The probability that the sample mean GPA is greater than 3.0 can be approximated by the area under the standard normal curve from 2.886 to infinity. This probability corresponds to approximately 0.0019 (or 0.19%).

Therefore, the approximate probability that, in a random sample of 25 students from this school, the sample mean GPA is greater than 3.0 is approximately 0.19%.