Thank you for the help Suppose you know that the heights of

Thank you for the help!

Suppose you know that the heights of elementary school students in southern Tanzania follow a probability distribution you dont know, except that the mean is 43.5 inches and the (population) standard deviation is 3.4 inches. You are planning to take a sample of 92 elementary school students, but have not yet. Approximately what is the probability that the mean score from this sample of 92 students is less than 43.3 inches?

Solution

Normal Distribution
Mean ( u ) =43.5
Standard Deviation ( sd )=3.4
Number ( n ) = 92
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X < 43.3) = (43.3-43.5)/3.4/ Sqrt ( 92 )
= -0.2/0.3545= -0.5642
= P ( Z <-0.5642) From Standard NOrmal Table
= 0.2863 ~ 28.63%