500 flights land each day at San Jose's airport. Assume that each flight has a 5% chance of being late, independently of whether any other flights are late. Using Excel, calculate the probability of the following events. Turn in your spreadsheet. (a) 15 or fewer flights are late. (b) 30 or more flights are late. (c) Exactly 26 flights are late. (d) Between 10 and 20 flights are late. (e) Does our assumption of independence seem reasonable to you? Why or why not?

a. 0.0199

b. 0.1765

c. 0.0785

d. 0.1268

e. Yes

Explanation:

It is given that X follows a Binomial distribution with (n = 500, p = 0.05)

The probabilities are computed using the EXCEL.

a) The required probability here is:

P (X less of equal to 15)

= binom. dist (15,500,0.05, TRUE)

=0.0199

Therefore the probability is 0.0199.

b) The required probability here is:

P (X greater or equal to 30) = 1 - P (X less or equal to 29)

=1 - binom. dist (29,500,0.05, TRUE)

=0.1765

Therefore the probability is 0.1765

c) P (X = 26)

= binom. dist (26,500,0.05, FALSE)

=0.0785

Therefore the probability is 0.0785

d) The required probability here is computed as:

P (10 less or equal to X less or equal to 20) = P (X less or equal to 19) - P (X less or equal to 10)

= binom. dist (19,500,0.05, TRUE) - binom. dist (10,500,0.05, TRUE)

=0.1268

Therefore the probability 0.1268

e) Yes. Therefore the probability because that is the assumption used to apply binomial distribution.