Question

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.

Answer 1

Ans:

Given that

n=10,p=0.85

P(x=r)=10C_r*0.85^r*(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