A study of the amounts of time college freshmen study each w

A study of the amounts of time college freshmen study each week found the distribution to be approximately normal with a mean of 7.06 hours and a standard deviation of 5.32 hours. If 55 freshmen are randomly selected, find the probability (correct to 2 decimal places) that their mean weekly study time exceeds 7.00 hours.

A. 0.48 B. 0.50 C. 0.53 D. 0.57

Solution

Mean ( u ) =7.06
Standard Deviation ( sd )=5.32
Number ( n ) = 55
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 7) = (7-7.06)/5.32/ Sqrt ( 55 )
= -0.06/0.717= -0.0836
= P ( Z >-0.0836) From Standard Normal Table
= 0.53