The average age of all students at a certain college is 22 years and the standard deviation is 2 years. What is the probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years

The probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years is 0.159

Step-by-step explanation:

According to the given data we have the following:

mean = μ = 22

standard deviation = σ = 2

n = 100

μx = 22

σx=σ/√n=2/√100=0.2

Therefore, P (x < 21.8) = P (x-μx) / σx< (21.8-22) / 0.2

=P (z<-1)

= 0.159

The probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years is 0.159