need explained please Suppose a university announced that it

need explained please

Suppose a university announced that it admitted 2,500 students for the following year\'s freshman class. However, the university has dorm room spots for only 1,780 freshman students. If there is a 70% chance that an admitted student will decide to accept the offer and attend this university, what is the approximate probability that the university will not have enough dormitory room spots for the freshman class?

Solution

Normal Distribution
Mean ( np ) =1750
Standard Deviation ( npq )= 2500*0.7*0.3 = 22.9129
Normal Distribution = Z= X- u / sd   

P(X < 1786) = (1786-1750)/22.9129
= 36/22.9129= 1.5712
= P ( Z <1.5712) From Standard NOrmal Table
= 0.9419                  
              
P(X >= 1786) = 1 - 0.9419 = 0.0582