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 of finding a sample mean less than 18 hours?
A)0.4820
B)0.4920
C)0.0080
D)0.0180

Question

Quizplus · Accepted Answer

We need to find the z-score first:
z = (x̄ - μ) / (σ / sqrt(n))
z = (18 - 20) / (10 / sqrt(144))
z = -2 / 0.833 = -2.4
Using a standard normal distribution table or calculator, we can find the probability of z-score being less than -2.4 is 0.008. Therefore, the probability of finding a sample mean less than 18 hours is 0.008.

A Group of Statistics Students Decided to Conduct a Survey