It is reported that 5 of students calculators fail during a

It is reported that 5% of students calculators fail during a test. 100 Students are taking a test, what is the probability that at least one will have their calculator fail? Using binomial normal approximation without continuity correction. (give your answer to three decimal places).

Solution

Here,

mean = n p = 100*0.05 = 5

standard deviation = sqrt(100*0.05*(1-0.05)) = 2.179449472

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    1      
u = mean =    5      
          
s = standard deviation =    2.179449472      
          
Thus,          
          
z = (x - u) / s =    -1.835325871      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.835325871   ) =    0.96677129 [ANSWER]