Question

The mean GPA for students is 2.7 with standard deviation .6. In a class of 30 students, what is the probability that the mean GPA for the class is less than 2.5? Assume the students in the classroom are a random sample of the population, and round the nearest hundredth.

Answer 1

X: GPA of student

Mean of X : =2.7

Standard deviation of X : =0.6

: Sample Mean  GPA for the class of 30 students (Sample size : n=30)

By central limit theorem follows normal with mean : =2.7 and standard deviation :

Probability that the mean GPA for the class is less than 2.5 = P(<2.5)

Z-score for 2.5 = (2.5 - 2.7)/0.1095 = -0.2/0.1095=-1.83

From standard normal tables,

P(Z<-1.83) = 0.0336

P(<2.5)=P(Z<-1.83) = 0.0336

Probability that the mean GPA for the class is less than 2.5 = P(<2.5)=0.0336