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 most one will have their calculator fail? Using binomial normal approximation without continuity correction. (give your answer to three decimal places).

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X < = 1) = P(X=1) + P(X=0)   
= ( 100 1 ) * 0.05^1 * ( 1- 0.05 ) ^99 + ( 100 0 ) * 0.05^0 * ( 1- 0.05 ) ^100
= 0.0371