A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students study 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 of finding a sample mean less than 18 hours?
A) 0.4820
B) 0.4918
C) 0.0082
D) 0.0181

Question

Quizplus · Accepted Answer

We can use the formula for the standard error of the mean:
standard error = standard deviation / sqrt(sample size)
= 10 / sqrt(144)
= 10 / 12
= 0.8333
Then, we can use the z-score formula to standardize our sample mean:
z-score = (sample mean - population mean) / standard error
= (18 - 20) / 0.8333
= -2.4
Looking up the area to the left of z = -2.4 in a standard normal distribution table (or calculator), we find the probability to be approximately 0.0082. Therefore, the answer is C.

A Group of Statistics Students Decided to Conduct a Survey