Cholesterol levels among 14year old boys are approximately n

Cholesterol levels among 14-year old boys are approximately normal with mean mu-170 and standard deviation o=30 mg/dl. If we select a random sample of 36 14-year old boys and consider the distribution of the sample mean X, find: the mean of X distribution, mu x the standard deviation of X distribution, sigma x the probability that sample mean X is 178 or more. mi = mu = 170 sigma 1 = sigma /squareroot N = 30 /squareroot 36 = 30 /6 = 5 p(x GE 178) = p/z GE (178) =

Solution

a)
Mean ( u ) =170
b)
Standard Deviation ( sd )=30/ Sqrt ( 36 ) = 30 / 6 = 5
Number ( n ) = 36
c)
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X < 178) = (178-170)/30/ Sqrt ( 36 )
= 8/5= 1.6
= P ( Z <1.6) From Standard NOrmal Table
= 0.9452                  
P(X > = 178) = 1 - P(X < 178)
= 1 - 0.9452 = 0.0548