Question

An advertising company routinely sends a survey to TV viewers to determine their opinion of the commercials it produces based on a scale of 0 – 10. The mean rating (m) on this survey over the past decade is 7.4 and the standard deviation (σ) is 2.2. If the company sends the survey to a sample of 100 viewers, what is the probability that the mean of this sample will be less than 7.0?

Answer 1

for normal distribution z score =(X-μ)/σ
here mean=       μ=	7.4
std deviation   =σ=	2.20
sample size       =n=	100
std error=σx̅=σ/√n=	0.22000

probability that the mean of this sample will be less than 7.0 :

probability =P(X<7)=(Z<(7-7.4)/0.22)=P(Z<-1.82)=0.0344