Question

eighty percent of the flights arriving in Atlanta for a large us airline are on time. if the faa randomly selects 50 of the airline's flights, find the probability that between 70% and 80% of the sampled flights will be on time.

Answer 1

Solution :

Given that ,

p = 0.80

1 - p = 0.20

n = 50

= p = 0.80

= (p*(1-p))/n =  (0.80*0.20)/ 50= 0.05657

P(0.70 < <0.80 ) = P((0.70-0.80)/0.05657 ) < ( - ) /  < (0.80-0.80) /0.05657 ) )

= P(-1.77 < z < 0 )

= P(z < 0) - P(z < -1.77)

= 0.5000 - 0.0384

= 0.4616

Probability = 0.4616

The probability that between 70% and 80% of the sampled flights will be on time is 0.4616