Question

A professor knows that her statistics students' final exam scores have a mean of 78 and a standard deviation of 9.3. In his class, an "A" is any exam score of 90 or higher. This quarter she has 25 students in her class. What is the probability that 4 students or more will score an "A" on the final exam?

Answer 1

µ =    78                  
σ =    9.3                  
                      
P ( X ≥   90   ) = P( (X-µ)/σ ≥ (90-78) / 9.3)              
= P(Z ≥   1.290   ) = P( Z <   -1.290   ) =    0.0985   (answer)

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Probability of getting A = 0.0985

n=25

and probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

P(X≥4) = 1-P(X<4) = 1 - P(X=0) -P(X=1) - P(X=3) = 0.2280

probability that 4 students or more will score an "A" on the final exam = 0.2280