Question

On average, only 95% of people bought an airline ticket will show up in the airport. In an airline’s flight, 400 people bought tickets. What is the probability that the number of people coming to the airport is at least 380 but no more than 390.

Answer 1

Solution:

Given that,

p = 95% = 0.95

n = 400

Here, BIN (400 , 0.95)

According to normal approximation binomial,

X Normal

Mean = = n*p = 400 * 0.95 = 380

Standard deviation = =n*p*(1-p) = [400*0.95*(1-0.95)] = 4.35889894354

Now ,

P(X is at least 380 but no more than 390)

= P[380 X 390]

= P[(380 - ) /   Z (390 - ) / ]

= P[(380 - 380) /4.35889894354   Z (390 - 380) /4.35889894354 ]

= P[0.00    Z 2.29]

= P[Z 2.29] - P[Z 0.00]

= 0.9890 - 0.5000

= 0.4890

Required Probability = 0.4890