Question

# According to an? airline, flights on a certain route are on time 8585?% of the time....

According to an? airline, flights on a certain route are on time
8585?%
of the time. Suppose
1010
flights are randomly selected and the number of on time flights is recorded. Use technology to find the probabilities. Use the Tech Help button for further assistance.
?(a) Determine whether this is a binomial experiment.
?(b) Find and interpret the probability that exactly
88
flights are on time.
?(c) Find and interpret the probability that at least
88
flights are on time.
?(d) Find and interpret the probability that fewer than
88
flights are on time.
?(e) Find and interpret the probability that between
66
and
88
?flights, inclusive, are on time.

Ans:

Given that

n=10,p=0.85

P(x=r)=10Cr*0.85r*(1-0.85)10-r

a)Yes,it is binomial distribution,as only two outcomes possible(whether on time or not) and independent trials.

b)

P(x=8)=10C8*0.858*0.152=0.2759

c)Use below table for calculations:

P(atleast 8)=P(x>=8)

=P(x=8)+P(x=9)+P(x=10)

=0.276+0.347+0.197

=0.820

d)P(x<8)=1-P(x>=8)=1-0.820=0.180

e)P(6<=x<=8)=P(x=6)+P(x=7)+P(x=8)

=0.040+0.130+0.276=0.446

 x p(x) 0 0.000 1 0.000 2 0.000 3 0.000 4 0.001 5 0.008 6 0.040 7 0.130 8 0.276 9 0.347 10 0.197