Question

1. There are eight flights from Minneapolis to St. Cloud each day. The probability that any one flight is late is 0.10. Using the binomial probability formula: a. what is the probability that none are late? b. what is the probability that 1 or more are late? c. what is the probability that exactly 1 flight is late? d. What is the probability that there are between 3 and 6 flights (both inclusive) that are late?

Answer 1

n=8

p=0.10

X=number of flight late

X~B(n,p)

Formula:

$p(x)=\binom{n}{x}p^{x}q^{n-x}$

a)Prob that none are late

P(x=0)

8 p(z = 0)-( ) 0.1000.908

P(x=0)=0.4305

b)Prob that one or more are late

P(X>=1)=1-P(x=0)

=1-0.4305

=0.5695

c)Prob that exactly one are late

P(x=1)

80.10 0.90

p(x=1)=0.3826

d)Prob that there are between 3 to 6 flight are late

P(3<=x<=6)=P(x=3)+P((x-4)+P(x=5)+P(x=6)

0.1030.90 + 0.10 0.90+ 0,10 0,90

=0.03306744+0.0045927+0.00040824+0.00002268

=0.03809