Question

The mean points obtained in an aptitude examination is 179 points with a variance of 225 . What is the probability that the mean of the sample would be less than 175 points if 77 exams are sampled? Round your answer to four decimal places.

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	179
std deviation   =σ=	15.000

sample size       =n=	77
std error=σx̅=σ/√n=	1.7094

probability =P(X<175)=(Z<(175-179)/1.709)=P(Z<-2.34)=0.0096