The total study time for a statistics assignment in a popula

The total study time for a statistics assignment in a population of college students was approximately Normally distributed with a mean of 6.49 hours and standard deviation of 1.05 hours. Suppose you plan to take an SRS of size 150 and compute the average study time. (a) What is the mean and standard deviation of your sample? (b) What is the probability of coming up with a sample that shows that they studied 6.0 hours or less?

Solution

a)
Mean ( u ) =6.49
Standard Deviation ( sd )=1.05/ Sqrt ( 150 )=0.0857
Number ( n ) = 150
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
b)
P(X < 6) = (6-6.49)/1.05/ Sqrt ( 150 )
= -0.49/0.0857= -5.7155
= P ( Z <-5.7155) From Standard NOrmal Table
= 0