Data has been analyzed from a recent study There are 25 subj

Data has been analyzed from a recent study. There are 25 subjects in the sample. The mean is 75, standard deviation is 4.7. Answer the following....

What is the probability of obtaining by chance the following:

a mean less than 72?

a mean less than 74?

a mean greater than 76?

and a mean greater than 78?

Solution

Normal Distribution
Mean ( u ) =75
Standard Deviation ( sd )=4.7
Number ( n ) = 25
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
a)
P(X < 72) = (72-75)/4.7/ Sqrt ( 25 )
= -3/0.94= -3.1915
= P ( Z <-3.1915) From Standard NOrmal Table
= 0.0007                  
b)
P(X < 74) = (74-75)/4.7/ Sqrt ( 25 )
= -1/0.94= -1.0638
= P ( Z <-1.0638) From Standard NOrmal Table
= 0.1437                  
c)
P(X > 76) = (76-75)/4.7/ Sqrt ( 25 )
= 1/0.94= 1.0638
= P ( Z >1.0638) From Standard Normal Table
= 0.1437                  
d)
P(X > 78) = (78-75)/4.7/ Sqrt ( 25 )
= 3/0.94= 3.1915
= P ( Z >3.1915) From Standard Normal Table
= 0.0007