28. A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the probability that a sample mean would exceed 20 hours per week?

A) 1.96
B) 0.5
C) Cannot be calculated based on the given information.
D) 1.0

To calculate the probability that a sample mean would exceed 20 hours per week, we need to use the concept of the standard deviation and the normal distribution.

Firstly, we know that the sample mean is 20 hours per week. Since we want to know the probability of a sample mean exceeding 20 hours, we are interested in the area under the normal curve to the right of this mean.

Secondly, we have the standard deviation, which is 10 hours. The standard deviation is a measure of how spread out the data is. It tells us how much we can expect individual data points to vary from the mean.

Now, we can calculate the probability using the z-score formula. The z-score is a measure of how many standard deviations a particular value is from the mean.

The formula for calculating the z-score is given by:
z = (x - μ) / (σ / √n)

Where:
z = z-score
x = sample mean we want to find the probability for (in this case, 20 hours)
μ = population mean (given as 20 hours)
σ = population standard deviation (given as 10 hours)
n = sample size (given as 144 students)

Plugging in the values:
z = (20 - 20) / (10 / √144)
z = 0 / (10 / 12)
z = 0

Now, we look up the z-score of 0 in the standard normal distribution table or use a calculator to find the corresponding probability.

By looking up the z-score of 0 in the standard normal distribution table, we find that the probability corresponding to a z-score of 0 is 0.5.

Therefore, the correct answer is B) 0.5.

If it is a normal distribution, mean = median = mode.

Look at your definition of median.