Final answer:
To find the probability that the mean time spent on academic activities is at least 28 hours per week, we need to use the standard deviation of the sample mean. The probability can be found by calculating the z-score and looking it up in the z-table or using a calculator.
Step-by-step explanation:
Question:
Full-time college students report spending a mean of 29 hours per week on academic activities, both inside and outside the classroom. Assume the standard deviation of time spent on academic activities is 5 hours. If you select a random sample of 25 full-time college students, what is the probability that the mean time spent on academic activities is at least 28 hours per week?
Answer:
To find the probability that the mean time spent on academic activities is at least 28 hours per week, we need to use the standard deviation of the sample mean. The standard deviation of the sample mean is equal to the population standard deviation divided by the square root of the sample size. In this case, the population standard deviation is 5 hours and the sample size is 25. So, the standard deviation of the sample mean is 5 / sqrt(25) = 1 hour. Now, we can use the z-score formula to find the probability: P(X >= 28) = P(Z >= (28 - 29) / 1) = P(Z >= -1) = 1 - P(Z < -1). We can look up the z-score (-1) in the z-table or use a calculator to find that the probability is approximately 0.1587. Therefore, the probability that the mean time spent on academic activities is at least 28 hours per week is 0.1587.