A simple random sample of size n 49 is obtained from a popu

A simple random sample of size n = 49 is obtained from a population with mu = 74 and sigma = 14. Describe the sampling distribution of x. What is P (x > 77.9)? What is P (x

Solution

a)
Mean ( u ) =74
Standard Deviation ( sd )=14
Number ( n ) = 49
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  

b)
P(X > 77.9) = (77.9-74)/14/ Sqrt ( 49 )
= 3.9/2= 1.95
= P ( Z >1.95) From Standard Normal Table
= 0.0256                  

c)
P(X < 69.1) = (69.1-74)/14/ Sqrt ( 49 )
= -4.9/2= -2.45
= P ( Z <-2.45) From Standard NOrmal Table
= 0.0071                  

d)
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 71.4) = (71.4-74)/14/ Sqrt ( 49 )
= -2.6/2
= -1.3
= P ( Z <-1.3) From Standard Normal Table
= 0.0968
P(X < 78.8) = (78.8-74)/14/ Sqrt ( 49 )
= 4.8/2 = 2.4
= P ( Z <2.4) From Standard Normal Table
= 0.9918
P(71.4 < X < 78.8) = 0.9918-0.0968 = 0.895