Homework SourseA group of statistics students decided to conduct a survey a
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 141 students. The statistics showed that students studied an average of 25 hours per week with a standard deviation of 12 hours. What is the probability that average student study time is between 23 and 27 hours?
A) 0.9522
B) 0.2440
C) 0.4880
D) 0.0239
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 141 students. The statistics showed that students studied an average of 25 hours per week with a standard deviation of 12 hours. What is the probability that average student study time is between 23 and 27 hours?
A) 0.9522
B) 0.2440
C) 0.4880
D) 0.0239
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 141 students. The statistics showed that students studied an average of 25 hours per week with a standard deviation of 12 hours. What is the probability that average student study time is between 23 and 27 hours?
A) 0.9522
B) 0.2440
C) 0.4880
D) 0.0239
Solution
let X be the random variable denoting the amount of time spent by students studying per week.
assuming X~N((25,122)
we have a sample of size n=141 from this population and Xbar be their average.
so Xbar~N((25,122/141)
now P[23<Xbar<27]=P[(23-25)/(12/sqrt(141))<(X-25)/(12/sqrt(141))<(27-25)/(12/sqrt(141))]
=P[-1.979<Z<1.979]
=P[Z<1.979]-P[Z<-1.979]=0.976092-0.0239080=0.9522 [option A] [answer]
